Università degli Studi di Trieste, Dipartimento di Matematica e Informatica
Rendiconti dell’Istituto di Matematica dell’Università di Trieste was founded in 1969 by Arno Predonzan, with the aim of publishing original research articles in all fields of mathematics and has been the first Italian mathematical journal to be published also on-line. The access to the electronic version of the journal is free. All published articles are available on-line. The journal can be obtained by subscription, or by reciprocity with other similar journals. Currently more than 100 exchange agreements with mathematics departments and institutes around the world have been entered in.
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.
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.
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.
Based on a recent characterization of the strong maximum principle, , this paper gives some periodic parabolic counterparts of some of the results of Chapters 8 and 9 of J. L´opez-G´omez . 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 , K. J. Brown and S. S. Lin , and P. Hess  on the existence and uniqueness of principal eigenvalues for weighted boundary value problems.