Nonconvex variational problem with recursive integral functionals in Sobolev spaces: Existence and representation

Integral functionals on Sobolev spaces having multiple local minima

THEOREM A. Let (X, τ) be a Hausdorff topological space and Ψ : X →]−∞,+∞], Φ : X → R two functions. Assume that there is r > infX Ψ such that the set Ψ (]−∞, r]) is compact and first-countable. Moreover, suppose that the function Φ is bounded below in Ψ(]−∞, r]) and that the function Ψ+ λΦ is sequentially lower semicontinuous for each λ ≥ 0 small enough. Finally, assume that the set of all glob...

Three Topological Problems about Integral Functionals on Sobolev Spaces

In this paper, I propose some problems, of topological nature, on the energy functional associated to the Dirichlet problem −∆u = f(x, u) in Ω, u|∂Ω = 0. Positive answers to these problems would produce innovative multiplicity results on this Dirichlet problem. In the present very short paper, I wish to propose some problems, of topological nature, on the energy functional associated to the Dir...

Stochastic homogenization of nonconvex integral functionals

— Almost sure epiconvergenee of a séquence of random intégral functionals is studied without convexity assumption. We give aproofby using an Ergodic theorem and recover and make précise the result of S. Muller in the periodic case. Finally, we study the asymptotic behaviour of corresponding random primai and dual problems in the convex case. Resumé. — Le problème étudié dans cet article concern...

A Representation for Characteristic Functionals of Stable Random Measures with Values in Sazonov Spaces

Existence Theorems for Nonconvex Variational Inequalities Problems

In this paper, we prove the existence theorem for a mapping defined by T = T1 + T2 when T1 is a μ1-Lipschitz continuous and γ-strongly monotone mapping, T2 is a μ2-Lipschitz continuous mapping, we have a mapping T is Lipschitz continuous but not strongly monotone mapping. This work is extend and improve the result of N. Petrot [17]. Mathematics Subject Classification: 46C05, 47D03, 47H09, 47H10...