OpenstarTshttps://www.openstarts.units.itThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Tue, 27 Oct 2020 12:42:26 GMT2020-10-27T12:42:26Z50491A periodic problem for first order differential equations with locally coercive nonlinearitieshttp://hdl.handle.net/10077/16219Title: A periodic problem for first order differential equations with locally coercive nonlinearities
Authors: Sovrano, Elisa; Zanolin, Fabio
Abstract: In this paper we study the periodic boundary value problem associated with a first order ODE of the form x' + g(t, x) = s where s is a real parameter and g is a continuous function, T-periodic in the variable t. We prove an Ambrosetti-Prodi type result in which the classical uniformity condition on g(t, x) at infinity is considerably relaxed. The Carathéodory case is also discussed.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162192017-01-01T00:00:00ZOn sheaves of differential operatorshttp://hdl.handle.net/10077/16220Title: On sheaves of differential operators
Authors: Massamba, Fortuné; Ntumba, Patrice P.
Abstract: Given a C∞ manifold X, denote by Cm / X the sheaf of m-times differentiable real-valued functions and by Dm,r / X the sheaf of differential operators of order ≤ m with coefficient functions of class C r . We prove that the natural morphism Dm−r,r / X → H omRX(Cm / X , Cr / X) is an isomorphism.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162202017-01-01T00:00:00ZGlobal stability, or instability, of positive equilibria of p-Laplacian boundary value problems with p-convex nonlinearitieshttp://hdl.handle.net/10077/16212Title: Global stability, or instability, of positive equilibria of p-Laplacian boundary value problems with p-convex nonlinearities
Authors: Rynne, Bryan P.
Abstract: We consider the parabolic, initial value problem
vt = Δp(v) + λg(x, v)φp(v), in Ω x (0,∞), v = 0, in ∂Ω x (0,∞), (IVP) v = v0 > 0, in Ω x {0}, where Ω is a bounded domain in RN , for some integer N > 1, with smooth boundary ∂Ω, φp(s) := |s|p−1 sgn s , s ∈ R , and Δp denotes the p -Laplacian, with p > max{2,N} , v0 ∈ C0(Ω) , and λ > 0 . The function g : Ω x [0,∞) → (0,∞) is C0 and, for each x ∈ Ω , the function g(x, ·) : [0,∞) → (0,∞) is Lipschitz continuous and strictly increasing.
Clearly, (IVP) has the trivial solution v ≡ 0 , for all λ > 0 . In addition, there exists 0 < λmin(g) < λmax(g) such that:
• if λ ∈/ (λmin(g),λmax(g)) then (IVP) has no non-trivial, positive
equilibrium;
• there exists a closed, connected set of positive equilibria bifurcating
from (λmax(g), 0) and ‘meeting infinity’ at λ = λmin(g) .
We prove the following results on the positive solutions of (IVP):
• if 0 < λ < λmin(g) then the trivial solution is globally asymptotically
stable;
• if λmin(g) < λ < λmax(g) then the trivial solution is locally asymptotically stable and all non-trivial, positive equilibria are unstable;
• if λmax(g) < λ then any non-trivial solution blows up in finite
time.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162122017-01-01T00:00:00ZBifurcation from infinity and multiplicity of solutions for nonlinear periodic boundary value problemshttp://hdl.handle.net/10077/16211Title: Bifurcation from infinity and multiplicity of solutions for nonlinear periodic boundary value problems
Authors: Mavinga, Nsoki; Nkashama, Mubenga N.
Abstract: We are concerned with multiplicity and bifurcation results for solutions of nonlinear second order diff erential equations with general linear part and periodic boundary conditions. We impose asymptotic conditions on the nonlinearity and let the parameter vary. We then proceed to establish a priori estimates and prove multiplicity results (for large-norm solutions) when the parameter belongs to a (nontrivial) continuum of real numbers. Our results extend and complement those in the literature. The proofs are based on degree theory, continuation methods, and bifurcation from infinity techniques.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162112017-01-01T00:00:00ZGauge-measurable functionshttp://hdl.handle.net/10077/16208Title: Gauge-measurable functions
Authors: Ponce, Augusto C.; Van Schaftingen, Jean
Abstract: In 1973, E. J. McShane introduced an alternative definition of the Lebesgue integral based on Riemann sums, where gauges are used to decide what tagged partitions are allowed. Such an approach does not require any preliminary knowledge of Measure Theory. We investigate in this paper a definition of measurable functions also based on gauges. Its relation to the gauge-integrable functions that satisfy McShane’s definition is obtained using elementary tools from Real Analysis. We show in particular a dominated integration property of gauge-measurable functions.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162082017-01-01T00:00:00ZSmoothness issues in differential equations with state-dependent delayhttp://hdl.handle.net/10077/16207Title: Smoothness issues in differential equations with state-dependent delay
Authors: Krisztin, Tibor; Walther, Hans-Otto
Abstract: For differential equations with state-dependent delays a satisfactory theory is developed by the second author [6] on the solution manifold to guarantee C1 -smoothness for the solution operators. We present examples showing that better than C1 -smoothness cannot be expected in general for the solution manifold and for local stable manifolds at stationary points on the solution manifold. Then we propose a new approach to overcome the diffi culties caused by the lack of smoothness. The mollification technique is used to approximate the nonsmooth evaluation map with smooth maps. Several examples show that the mollified systems can have nicer smoothness properties than the original equation. Examples are also given where better smoothness than C1 can be obtained on the solution manifold.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162072017-01-01T00:00:00ZOn general properties of n-th order retarded functional differential equationshttp://hdl.handle.net/10077/16206Title: On general properties of n-th order retarded functional differential equations
Authors: Benevieri, Pierluigi; Calamai, Alessandro; Furi, Massimo; Pera, Maria Patrizia
Abstract: Consider the second order RFDE (retarded functional differential equation) x’’ (t) = f(t, xt), where f is a continuous realvalued function defined on the Banach space R x C1([−r, 0],R). The weak assumption of continuity on f (due to the strong topology of C1([−r, 0],R)) makes not convenient to transform this equation into a first order RFDE of the type z’ (t) = g(t, zt). In fact, in this case, the associated R2-valued function g could be discontinuous (with the C0- topology) and, in addition, not necessarily defined on the whole space R x C([−r, 0],R2). Consequently, in spite of what happens for ODEs, the classical results regarding existence, uniqueness, and continuous dependence on data for first order RFDEs could not apply. Motivated by this obstruction, we provide results regarding general properties, such as existence, uniqueness, continuous dependence on data and continuation of solutions of RFDEs of the type x(n)(t) = f(t, xt), where f is an Rk-valued continuous function on the Banach space R x C(n−1)([−r, 0],Rk). Actually, for the sake of generality, our investigation will be carried out in the case of infinite delay.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162062017-01-01T00:00:00ZPositive and nodal single-layered solutions to supercritical elliptic problems above the higher critical exponentshttp://hdl.handle.net/10077/16205Title: Positive and nodal single-layered solutions to supercritical elliptic problems above the higher critical exponents
Authors: Clapp, Mónica; Rizzi, Matteo
Abstract: We study the problem −Δv + λv = |u|p−2 u in Ω, u= 0 on ∂Ω, for λ ∈ R and supercritical exponents p, in domains of the form Ω := {(y, z) ∈ RN−m−1 x Rm+1 : (y, |z|) ∈ Θ}, where m ≥ 1, N − m ≥ 3, and Θ is a bounded domain in RN−m whose closure is contained in RN−m−1 x (0,∞). Under some symmetry assumptions on Θ, we show that this problem has infinitely many solutions for every λ in an interval which contains [0,∞) and p > 2 up to some number which is larger than the (m+1)st critical exponent 2∗N,m := 2(N−m)/N−m−2 . We also exhibit domains with a shrinking hole, in which there are a positive and a nodal solution which concentrate on a sphere, developing a single layer that blows up at an m dimensional sphere contained in the boundary of Ω, as the hole shrinks and p → 2∗N,m from above. The limit profile of the positive solution, in the transversal direction to the sphere of concentration, is a rescaling of the standard bubble, whereas that of the nodal solution is a rescaling of a nonradial sign-changing solution to the problem −Δu = |u|2∗n−2 u, u ∈ D1,2(Rn), where 2∗n := 2n n−2 is the critical exponent in dimension n.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162052017-01-01T00:00:00ZOn the existence of nontrivial solutions of differential equations subject to linear constraintshttp://hdl.handle.net/10077/16203Title: On the existence of nontrivial solutions of differential equations subject to linear constraints
Authors: Schmitt, Klaus
Abstract: The purpose of this paper is to consider boundary value problems for second order ordinary diff erential equations where the solutions sought are subject to a host of linear constraints (such as multipoint constraints) and to present a unifying framework for studying such. We show how Leray-Schauder continuation techniques may be used to obtain existence results for nontrivial solutions of a variety of nonlinear second order diff erential equations. A typical example may be found in studies of the four-point boundary value problem for the diff erential equation y’’(t)+a(t)f(y(t)) = 0 on [0, 1], where the values of y at 0 and 1 are each some multiple of y(t) at two interior points of (0, 1). The techniques most often used in such studies have their origins in fixed point theory. By embedding such problems into parameter dependent ones, we show that detailed information may be obtained via global bifurcation theory. Of course, such techniques, as they are consequences of properties of the topological degree, are similar in nature.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162032017-01-01T00:00:00ZPositive decaying solutions to BVPs with mean curvature operatorhttp://hdl.handle.net/10077/16210Title: Positive decaying solutions to BVPs with mean curvature operator
Authors: Došlá, Zuzana; Marini, Mauro; Matucci, Serena
Abstract: A boundary value problem on the whole half-closed interval [1,∞) , associated to diff erential equations with the Euclidean mean curvature operator or with the Minkowski mean curvature operator is here considered. By using a new approach, based on a linearization device and some properties of principal solutions of certain disconjugate second-order linear equations, the existence of global positive decaying solutions is examined.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162102017-01-01T00:00:00ZHamilton-Jacobi on the symplectic grouphttp://hdl.handle.net/10077/16209Title: Hamilton-Jacobi on the symplectic group
Authors: Ekeland, Ivar
Abstract: The classical Hamilton-Jacobi-Bellman theory in the calculus of variations, which is associated with the Bolza problem, is extended to other kinds of boundary-value problems, such as periodicity. By using the dual action principle of Clarke and earlier results by the author, one can establish the analogue of HJB on the symplectic group and show that it has a solution.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162092017-01-01T00:00:00ZPrincipal eigenvalues of weighted periodic-parabolic problemshttp://hdl.handle.net/10077/16217Title: Principal eigenvalues of weighted periodic-parabolic problems
Authors: Antón, Inmaculada; López-Gómez, Julián
Abstract: Based on a recent characterization of the strong maximum principle, [3], this paper gives some periodic parabolic counterparts of some of the results of Chapters 8 and 9 of J. L´opez-G´omez [22]. Among them count some pivotal monotonicity properties of the principal eigenvalue σ[P+V,B,QT ], as well as its concavity with respect to the periodic potential V through a point-wise periodic-parabolic Donsker–Varadhan min-max characterization. Finally, based on these findings, this paper sharpens, substantially, some classical results of A. Beltramo and P. Hess [4], K. J. Brown and S. S. Lin [6], and P. Hess [14] on the existence and uniqueness of principal eigenvalues for weighted boundary value problems.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162172017-01-01T00:00:00ZFlat solutions of the 1-Laplacian equationhttp://hdl.handle.net/10077/16204Title: Flat solutions of the 1-Laplacian equation
Authors: Orsina, Luigi; Ponce, Augusto C.
Abstract: Abstract. For every f ∈ Ln(Ω) defined in an open bounded subset Ω of Rn, we prove that a solution u ∈ W01,1 (Ω) of the 1-Laplacian equation – div (∇u / |∇u|)= f in Ω satisfies ∇u = 0 on a set of positive Lebesgue measure. The same property holds if f ∈/ Ln(Ω) has small norm in the Marcinkiewicz space of weak–Ln functions or if u is a BV minimizer of the associated energy functional. The proofs rely on Stampacchia’s truncation method.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162042017-01-01T00:00:00ZRemarks on nonautonomous bifurcation theoryhttp://hdl.handle.net/10077/16214Title: Remarks on nonautonomous bifurcation theory
Authors: Franca, Matteo; Johnson, Russell
Abstract: We study some elementary bifurcation patterns when the bifurcation parameter is subjected to fast oscillations.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162142017-01-01T00:00:00ZPositive radial solutions for systems with mean curvature operator in Minkowski spacehttp://hdl.handle.net/10077/16215Title: Positive radial solutions for systems with mean curvature operator in Minkowski space
Authors: Gurban, Daniela; Jebelean, Petru
Abstract: We are concerned with a Dirichlet system, involving the mean curvature operator in Minkowski space
M(w) = div (∇w / 1−|∇w|2)
in a ball in RN. Using topological degree arguments, critical point theory and lower and upper solutions method, we obtain non existence, existence and multiplicity of radial, positive solutions. The examples we provide involve Lane-Emden type nonlinearities in both sublinear and superlinear cases.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162152017-01-01T00:00:00ZThe Semilinear Wave Equation with Non-Monotone Nonlinearity: A Reviewhttp://hdl.handle.net/10077/16213Title: The Semilinear Wave Equation with Non-Monotone Nonlinearity: A Review
Authors: Caicedo, Francisco; Castro, Alfonso; Duque, Rodrigo; Sanjuán, Arturo
Abstract: We review recent results on the existence of weak 2π- periodic solutions in time and space for a class of semilinear wave equations with non-monotone nonlinearity. Similar results exist for Dirichlet-periodic boundary conditions but, for the sake of clarity, we exclude them in this presentation.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162132017-01-01T00:00:00ZOn a family of Kepler problems with linear dissipationhttp://hdl.handle.net/10077/16216Title: On a family of Kepler problems with linear dissipation
Authors: Margheri, Alessandro; Ortega, Rafael; Rebelo, Carlota
Abstract: We consider the dissipative Kepler problem for a family of dissipations that is linear in the velocity. Under mild assumptions on the drag coefficient, we show that its forward dynamics is qualitatively similar to the one obtained in [15] and [16] for a constant drag coefficient. In particular, we extend to this more general framework the existence of a continuous vector-valued first integral I obtained as the limit along the trajectories of the Runge-Lenz vector. We also establish the existence of asymptotically circular orbits, so improving the result about the range of I contained in [16].
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162162017-01-01T00:00:00ZDirichlet problems without asymptotic conditions on the nonlinear termhttp://hdl.handle.net/10077/16218Title: Dirichlet problems without asymptotic conditions on the nonlinear term
Authors: Bonanno, Gabriele
Abstract: This paper is devoted, with my great esteem, to Jean Mawhin. Jean Mawhin, who is for me a great teacher and a very good friend, is a fundamental reference for the research in nonlinear differential problems dealt both with topological and variational methods. Here, owing to this occasion in honor of Jean Mawhin, Dirichlet problems depending on a parameter are investigated, ensuring the existence of non-zero solutions without requiring asymptotic conditions neither at zero nor at infinity on the nonlinear term which, in addition, is not forced by subcritical or critical growth. The approach is based on a combination of variational and topological tools that in turn are developed by starting from a fundamental estimate.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10077/162182017-01-01T00:00:00ZRendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 51 (2019)http://hdl.handle.net/10077/29413Title: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 51 (2019)
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10077/294132019-01-01T00:00:00ZRendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)http://hdl.handle.net/10077/30804Title: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol. 52 (2020)
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/308042020-01-01T00:00:00ZConvexity, topology and nonlinear differential systems with nonlocal boundary conditionshttp://hdl.handle.net/10077/29333Title: Convexity, topology and nonlinear differential systems with nonlocal boundary conditions
Authors: Mawhin, Jean; Szymanska-Debowska, Katarzyna
Abstract: This paper is a survey of recent existence results for solutions of first and second order nonlinear differential systems with nonlocal boundary conditions using methods based upon convexity, topological degree and maximum-principle like techniques.
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10077/293332019-01-01T00:00:00ZRealizations of certain odd-degree surface branch datahttp://hdl.handle.net/10077/30767Title: Realizations of certain odd-degree surface branch data
Authors: Petronio, Carlo
Abstract: We consider surface branch data with base surface the sphere, odd degree d, three branching points, and partitions of d of the form
(2, ..., 2, 1) (2,..., 2, 2h + 1) π
with π having length ℓ. This datum satisfies the Riemann-Hurwitz necessary condition for realizability if h — ℓ is odd and at least —1. For several small values of h and ℓ (namely, for h + ℓ ≤ 5) we explicitly compute the number v of realizations of the datum up to the equivalence relation given by the action of automorphisms (even unoriented ones) of both the base and the covering surface. The expression of v depends on arithmetic properties of the entries of π. In particular we find that in the only case where v is 0 the entries of π have a common divisor, in agreement with a conjecture of Edmonds-Kulkarny-Stong and a stronger one of Zieve.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307672020-01-01T00:00:00ZOn upper and lower bounds for finite group-actions on bounded surfaces, handlebodies, closed handles and finite graphshttp://hdl.handle.net/10077/29334Title: On upper and lower bounds for finite group-actions on bounded surfaces, handlebodies, closed handles and finite graphs
Authors: Zimmermann, Bruno P.
Abstract: In the present paper, partly a survey, we discuss upper and lower bounds for finite group-actions on bounded surfaces, 3-dimensional handlebodies and closed handles, handlebodies in arbitrary dimensions and finite graphs (the common feature of these objects is that they have all free fundamental group).
Tue, 01 Jan 2019 00:00:00 GMThttp://hdl.handle.net/10077/293342019-01-01T00:00:00ZNon-isometric hyperbolic 3-orbifolds with the same topological type and volumehttp://hdl.handle.net/10077/30766Title: Non-isometric hyperbolic 3-orbifolds with the same topological type and volume
Authors: Los, Jérôme; Paoluzzi, Luisa; Salgueiro, António
Abstract: We construct pairs of non-isometric closed hyperbolic 3-orbifolds with the same topological type and volume. Topologically these orbifolds are mapping tori of pseudo-Anosov maps of the surface of genus 2, with singular locus a fibred (hyperbolic) link with five components.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307662020-01-01T00:00:00ZConnectivity results for surface branched ideal triangulationshttp://hdl.handle.net/10077/30755Title: Connectivity results for surface branched ideal triangulations
Authors: Benedetti, Riccardo
Abstract: We consider triangulations of closed surfaces S with a given set of vertices V ; every triangulation can be branched that is enhanced to be a Δ-complex. Branched triangulations are considered up to the b-transit equivalence generated by b-flips (i.e. branched diagonal exchanges) and isotopy keeping V pointwise fixed. We extend a well-known connectivity result for 'naked' triangulations; in particular, in the generic case when χ(S) < 0, we show that each branched triangulation is connected to any other if χ(S) is even, while this holds also for odd χ(S) possibly after the complete inversion of one of the two branchings. Natural distribution of the b-flips in sub-families gives rise to restricted transit equivalences with nontrivial (even infinite) quotient sets. We analyze them in terms of certain structures of geometric/topological nature carried by each branched triangulation, invariant for the given restricted equivalence.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307552020-01-01T00:00:00ZComplicated dynamics in a model of charged particleshttp://hdl.handle.net/10077/30761Title: Complicated dynamics in a model of charged particles
Authors: Gjata, Oltiana; Zanolin, Fabio
Abstract: We give an analytical proof of the presence of complex dynamics for a model of charged particles in a magnetic field. Our method is based on the theory of topological horseshoes and applied to a periodically perturbed Dffing equation. The existence of chaos is proved for sufficiently large, but explicitly computable, periods.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307612020-01-01T00:00:00ZStability and periodicity of solutions to the Oldroyd-B model on exterior domainshttp://hdl.handle.net/10077/30762Title: Stability and periodicity of solutions to the Oldroyd-B model on exterior domains
Authors: Hieber, Matthias; Nguyen, Thieu Huy
Abstract: Consider the Oldroyd-B system on exterior domains with nonzero external forces f. It is shown that this system admits under smallness assumptions on f a bounded, global solution (u; τ), which is stable in the sense that any other global solution to this system starting in a sufficiently small neighborhood of (u(0); τ (0)) is tending to (u; τ). In addition, if the outer force is T-periodic and small enough, the Oldroyd-B system admits a T-periodic solution. Note that no smallness condition on the coupling coefficient is assumed.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307622020-01-01T00:00:00ZBoundedness of solutions to the Cauchy problem for an attraction-repulsion chemotaxis system in two-dimensional spacehttp://hdl.handle.net/10077/30765Title: Boundedness of solutions to the Cauchy problem for an attraction-repulsion chemotaxis system in two-dimensional space
Authors: Nagai, Tetsutaka; Yamada, Tetsuya
Abstract: We consider the Cauchy problem for an attraction-repulsion chemotaxis system in two-dimensional space. The system consists of three partial differential equations; a drift-diffusion equation incorporating terms for both chemoattraction and chemorepulsion, and two elliptic equations. We denote by β1 the coefficient of the attractant and by β2 that of the repellent. The boundedness of nonnegative solutions to the Cauchy problem was shown in the repulsive dominant case β1 < β2 and the balance case β1 = β2. In this paper, we study the boundedness problem to the Cauchy problem in the attractive dominant case β1 > β2.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307652020-01-01T00:00:00ZGlobal structure of bifurcation curves related to inverse bifurcation problemshttp://hdl.handle.net/10077/30768Title: Global structure of bifurcation curves related to inverse bifurcation problems
Authors: Shibata, Tetsutaro
Abstract: We consider the nonlinear eigenvalue problem
[D(u(t))u(t)']' + λg(u(t)) = 0,
u(t) > 0 ; t ∈ I := (0, 1), u(0) = u(1) = 0,
which comes from the porous media type equation. Here, D(u) = pu2n+sin u (n ∈ N, p > 0: given constants), g(u) = u or g(u) = u + sin u. λ > 0 is a bifurcation parameter which is a continuous function of α = ||uλ||∞ of the solution uλ corresponding to λ, and is expressed as λ = λ(α). Since our equation contains oscillatory term in diffusion term, it seems significant to study how this oscillatory term gives effect to the structure of bifurcation curves λ(α). We propose a question from a view point of inverse bifurcation problems and show that the simplest case D(u) = u2 + sin u and g(u) = u gives us the most impressible asymptotic formula for global behavior of λ(α).
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307682020-01-01T00:00:00ZA spatiotemporal model of drug resistance in bacteria with mutationshttp://hdl.handle.net/10077/30763Title: A spatiotemporal model of drug resistance in bacteria with mutations
Authors: Hsu, Sze-Bi; Jiang, Jifa
Abstract: A spatio-temporal dynamics model is presented to study the effects of mutations on the persistence and extinction of bacteria under the antibiotic inhibition. We construct a mixed type Lyapunov functional to prove the global stability of extinction state and coexistence state for the case of forward mutation and forward-backward mutation respectively.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307632020-01-01T00:00:00ZCrystallizations of compact 4-manifolds minimizing combinatorially de ned PL-invariantshttp://hdl.handle.net/10077/30760Title: Crystallizations of compact 4-manifolds minimizing combinatorially de ned PL-invariants
Authors: Casali, Maria Rita; Cristofori, Paola; Gagliardi, Carlo
Abstract: The present paper is devoted to present a unifying survey about some special classes of crystallizations of compact PL 4-manifolds with empty or connected boundary, called semi-simple and weak semi-
simple crystallizations, with a particular attention to their properties of minimizing combinatorially defined PL-invariants, such as the regular genus, the Gurau degree, the gem-complexity and the (gem-induced)
trisection genus. The main theorem, yielding a summarizing result on the topic, is an original contribution. Moreover, in the present paper the additivity of regular genus with respect to connected sum is proved to hold for all compact 4-manifolds with empty or connected boundary which admit weak semi-simple crystallizations.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307602020-01-01T00:00:00ZPopulation dynamics in hostile neighborhoodshttp://hdl.handle.net/10077/30754Title: Population dynamics in hostile neighborhoods
Authors: Amann, Herbert
Abstract: A new class of quasilinear reaction-diffusion equations is introduced for which the mass flow never reaches the boundary. It is proved that the initial value problem is well-posed in an appropriate weighted Sobolev space setting.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307542020-01-01T00:00:00ZCanonical Cohen-Macaulay property and Lyubeznik numbers under Gröbner deformationshttp://hdl.handle.net/10077/30764Title: Canonical Cohen-Macaulay property and Lyubeznik numbers under Gröbner deformations
Authors: Nadi, Parvaneh; Varbaro, Matteo
Abstract: In this note we draw some interesting consequences of the recent results on squarefree Gröbner degenerations obtained by Conca and the second author.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307642020-01-01T00:00:00ZAsymptotic properties of a free boundary problem for a reaction-di usion equation with multi-stable nonlinearityhttp://hdl.handle.net/10077/30771Title: Asymptotic properties of a free boundary problem for a reaction-di usion equation with multi-stable nonlinearity
Authors: Yamada, Yoshio
Abstract: This paper deals with a free boundary problem for a reaction-diffusion equation with moving boundary, whose dynamics is governed by the Stefan condition. We will mainly discuss the problem for the case of multi-stable nonlinearity, which is a function with a multiple number of positive stable equilibria. The first result is concerned with the classi cation of solutions in accordance with large-time behaviors. As a consequence, one can observe a multiple number of spreading phenomena corresponding for each positive stable equilibrium. Here it is seen that there exists a certain group of spreading solutions whose element accompanies a propagating terrace. We will derive sharp asymptotic estimates of free boundary and profile of every spreading solution including spreading one with propagating terrace.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307712020-01-01T00:00:00ZNon-standard bifurcation approach to nonlinear elliptic problemshttp://hdl.handle.net/10077/30769Title: Non-standard bifurcation approach to nonlinear elliptic problems
Authors: Cintra, W.; Morales-Rodrigo, C.; Suarez, A.
Abstract: Bifurcation is a very useful method to prove the existence of positive solutions for nonlinear elliptic equations. The existence of an unbounded continuum of positive solutions emanating from zero or from infinity can be deduced in many problems. In this paper, we show the applicability of this method in some problems where the classical bifurcation results can not be directly applied.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307692020-01-01T00:00:00ZHalf-unknotted 2-orbifolds in orientable spherical 3-orbifoldshttp://hdl.handle.net/10077/30770Title: Half-unknotted 2-orbifolds in orientable spherical 3-orbifolds
Authors: Wang, Chao
Abstract: If an embedding of a 2-orbifold in an orientable spherical 3-orbifold splits the 3-orbifold into two parts such that at least one part is a handlebody orbifold, then we call it half-unknotted. We will give different kinds of algebraic conditions on the embedding such that it is half-unknotted. The results will be applied to questions about extendable actions on surfaces. As an example, we will show that embeddings realizing the maximum order of extendable cyclic actions on genus g > 1 surfaces must be unknotted.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/307702020-01-01T00:00:00ZA collocation-spectral method to solve the bi-dimensional degenerate diffusive logistic equation with spatial heterogeneities in circular domainhttp://hdl.handle.net/10077/30917Title: A collocation-spectral method to solve the bi-dimensional degenerate diffusive logistic equation with spatial heterogeneities in circular domain
Authors: Molina-Meyer, Marcela; Prieto Medina, Frank Richard
Abstract: In this paper we simulate positive solutions, large solutions and metasolutions of the heterogeneous logistic equation in a disk and an annulus. The numerical methods introduced in this paper are extremely innovative because they make unnecessary determining any previous lifting and solving any decoupled system of ordinary differential equations. Moreover, they can be used to solve non-radially symmetric problems. The models are of a huge interest in Spatial Ecology because they enable us to analyse the effects of the spatial heterogeneity on the evolution of the terrestrial ecosystems. The large solutions and the metasolutions have been computed by the first time in this paper.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309172020-01-01T00:00:00ZInfluence of the spatial heterogeneities in the existence of positive solutions logistic BVPs with sublinear mixed boundary conditionshttp://hdl.handle.net/10077/30911Title: Influence of the spatial heterogeneities in the existence of positive solutions logistic BVPs with sublinear mixed boundary conditions
Authors: Cano-Casanova, Santiago
Abstract: In this paper we analyze the influence of the spatial heterogeneities
in the existence of positive solutions of Logistic problems
with heterogeneous sublinear boundary conditions. We will show that
the relative positions of the vanishing sets of the potentials in front of
the nonlinearities, in the PDE and on the boundary conditions, play a
crucial role as for the amplitude of the range of values of the bifurcation
parameter for which the problems possess positive solutions. We
will compare the cases of the logistic problem with linear and nonlinear
boundary conditions. Also, we will show the global bifurcation diagram
of positive solutions of the logistic problem with heterogeneous nonlinear
boundary conditions, considering the amplitude of the nonlinearity
in the boundary conditions as bifurcation-continuation parameter.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309112020-01-01T00:00:00ZNumerical global bifurcation diagrams for a superlinear indefinite problem with a parameter appearing in the domainhttp://hdl.handle.net/10077/30916Title: Numerical global bifurcation diagrams for a superlinear indefinite problem with a parameter appearing in the domain
Authors: Tellini, Andrea
Abstract: We consider a superlinear indefinite problem with homogeneous Neumann boundary conditions and a parameter appearing in the domain of the di erential equation. Such a problem is an extension of the one studied in [33], in the sense that also negative values of the parameter are allowed.
First, we show how to discretize the problem in a way that is suitable to perform numerical continuation methods and obtain the associated bifurcation diagrams. Then, we analyze the results of the simulations, also studying the stability of the solutions.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309162020-01-01T00:00:00ZPast and recent contributions to indefinite sublinear elliptic problemshttp://hdl.handle.net/10077/30913Title: Past and recent contributions to indefinite sublinear elliptic problems
Authors: Kaufmann, U.; Ramos Quoirin, H.; Umezu, K.
Abstract: We review the inde nite sublinear elliptic equation Δu =a(x)u<sup>q</sup> in a smooth bounded domain ΩCR<sup>N</sup>, with Dirichlet or Neumann homogeneous boundary conditions. Here 0 < q < 1 and a is continuous and changes sign, in which case the strong maximum principle does not apply. As a consequence, the set of nonnegative solutions of these problems has a rich structure, featuring in particular both dead core and/or positive solutions. Overall, we are interested in su_x000E_cient and necessary conditions on a and q for the existence of positive solu-
tions. We describe the main results from the past decades, and combine it with our recent contributions. The proofs are briefly sketched.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309132020-01-01T00:00:00ZA note on a class of double well potential problemshttp://hdl.handle.net/10077/30912Title: A note on a class of double well potential problems
Authors: Montecchiari, Piero; Rabinowitz, Paul H.
Abstract: It is well known that under appropriate conditions on a double well potential, the associated Hamiltonian system possesses a
pair of heteroclinic solutions joining the minima of the potential in addition to in nitely many other homoclinics and heteroclinics that oscillate between these minima. This paper studies the effect on such solutions of replacing the temporal domain, R, by a nite but long time interval.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309122020-01-01T00:00:00ZExistence of attractors when diffusion and reaction have polynomial growthhttp://hdl.handle.net/10077/30915Title: Existence of attractors when diffusion and reaction have polynomial growth
Authors: Ahmad, Shair; Le, Dung
Abstract: We study an interesting model, with reaction terms of Lotka-Volterra type, where diffusion and reaction have polynomial growth of any order. We establish existence of global attractors as well as exponential attractors. In the sequel we study the long time dynamics of an appropriate semigroup and show that it possesses a global attractor (and exponential attractors) in a certain Banach space.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309152020-01-01T00:00:00ZTetrahedral Coxeter groups, large group-actions on 3-manifolds and equivariant Heegaard splittingshttp://hdl.handle.net/10077/30923Title: Tetrahedral Coxeter groups, large group-actions on 3-manifolds and equivariant Heegaard splittings
Authors: Zimmermann, Bruno P.
Abstract: We consider finite group-actions on closed, orientable and nonorientable 3-manifolds M which preserve the two handlebodies of a Heegaard splitting of M of some genus g > 1 (maybe interchanging the two handlebodies). The maximal possible order of a finite group-action on a handlebody of genus g > 1 is 12(g — 1) in the orientation-preserving case and 24(g — 1) in general, and the maximal order of a finite group preserving the Heegaard surface of a Heegaard splitting of genus g is 48(g —1). This defines a hierarchy for finite group-actions on 3-manifolds which we discuss in the present paper; we present various manifolds with an action of type 48(g — 1) for small values of g, and in particular the unique hyperbolic 3-manifold with such an action of smallest possible genus g = 6 (in strong analogy with the Euclidean case of the 3-torus which has such actions for g = 3).
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309232020-01-01T00:00:00ZOn the diffeomorphism type of Seifert fibered spherical 3-orbifoldshttp://hdl.handle.net/10077/30920Title: On the diffeomorphism type of Seifert fibered spherical 3-orbifolds
Authors: Mecchia, Mattia; Seppi, Andrea
Abstract: It is well known that, among closed spherical Seifert three-manifolds, only lens spaces and prism manifolds admit several Seifert fibrations which are not equivalent up to diffeomorphism. Moreover the former admit infinitely many fibrations, and the latter exactly two. In this work, we analyse the non-uniqueness phenomenon for orbifold Seifert fibrations. For any closed spherical Seifert three-orbifold, we determine the number of its inequivalent fibrations. When these are in finite number (in fact, at most three) we provide a complete list. In case of infinitely many fibrations, we describe instead an algorithmic procedure to determine whether two closed spherical Seifert orbifolds are diffeomorphic.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309202020-01-01T00:00:00ZClassifiation of parabolic generating pairs of Kleinian groups with two parabolic generatorshttp://hdl.handle.net/10077/30919Title: Classifiation of parabolic generating pairs of Kleinian groups with two parabolic generators
Authors: Aimi, Shunsuke; Lee, Donghi; Sakai, Shunsuke; Sakuma, Makoto
Abstract: We give an alternative proof to Agol's classification of parabolic generating pairs of non-free Kleinian groups generated by two parabolic transformations. As an application, we give a complete characterisation of epimorphims between 2-bridge knot groups and a complete characterisation of degree one maps between the exteriors of hyperbolic 2-bridge links.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309192020-01-01T00:00:00ZTwo Moore's theorems for graphshttp://hdl.handle.net/10077/30918Title: Two Moore's theorems for graphs
Authors: Mednykh, Alexander; Mednykh; Ilya
Abstract: Let X be a finite connected graph, possibly with loops and multiple edges. An automorphism group of X acts purely harmonically if it acts freely on the set of directed edges of X and has no invertible edges. Dene a genus g of the graph X to be the rank of the first homology group. A finite group acting purely harmonically on a graph of genus g is a natural discrete analogue of a finite group of automorphisms acting on a Riemann surface of genus g: In the present paper, we investigate cyclic group Z<sub>n</sub> acting purely harmonically on a graph X of genus g with fixed points. Given subgroup Z<sub>d</Sub> < Z<sub>n</sub>; we find the signature of orbifold X=Z<sub>d</sub> through the signature of orbifold X=Z<sub>n</sub>: As a result, we obtain formulas for the number of fixed points for generators of group Z<sub>d</sub> and for genus of orbifold X=Z<sub>d</sub>: For Riemann surfaces, similar results were obtained earlier by M. J. Moore.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309182020-01-01T00:00:00ZNonlinear boundary value problems relative to the one dimensional heat equationhttp://hdl.handle.net/10077/30914Title: Nonlinear boundary value problems relative to the one dimensional heat equation
Authors: Véron, Laurent
Abstract: We consider the problem of existence of a solution u to δ<sub>t</sub>u — δ<sub>xx</sub>u = 0 in (0, T) x R<sub>+</sub> subject to the boundary condition — u<sub>x</sub>(t,0) + g(u(t, 0)) = μ on (0, T) where μ is a measure on (0, T) and g a continuous nondecreasing function. When p > 1 we study the set of self-similar solutions of δ<sub>t</sub>u — δ<sub>xx</sub>u = 0 in R<sub>+</sub> — R<sub>+</sub> such that —u<sub>x</sub>(t,0)+u<sup>p</sup> = 0 on (0,∞). At end, we present various extensions to a higher dimensional framework.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309142020-01-01T00:00:00ZA small collection of open problemshttp://hdl.handle.net/10077/30921Title: A small collection of open problems
Authors: Alessandrini, Giovanni
Abstract: This paper collects some problems that I have encountered during the years, have puzzled me and which, to the best of my knowledge, are still open. Most of them are well-known and have been first stated by other authors. In this sad season of pandemic, I modestly try to contribute to scientic interaction at a distance. Therefore all comments and exchange of information are most welcome.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309212020-01-01T00:00:00ZTensor decompositions in rank +1http://hdl.handle.net/10077/30922Title: Tensor decompositions in rank +1
Authors: Ballico, Edoardo
Abstract: We prove (without exceptions) the existence of irredundant tensor decompositions with the number of addenda equal to rank +1. We also discuss the existence of decompositions with more than the tensor rank terms, which are concise, while the original tensor is not concise.
Wed, 01 Jan 2020 00:00:00 GMThttp://hdl.handle.net/10077/309222020-01-01T00:00:00Z