OpenstarTshttps://www.openstarts.units.itThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Fri, 05 Jun 2020 00:54:21 GMT2020-06-05T00:54:21Z50211A 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/10077/294132019-01-01T00:00:00ZConvexity, 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/10077/293332019-01-01T00:00:00ZOn 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/10077/293342019-01-01T00:00:00Z