Generalized Fountain Theorem for Locally Lipschitz Functionals and application

Abstract

In this paper, we obtain a nonsmooth version of the infinite-dimensional Fountain Theorem established by Batkam and Colin (2013). No symmetry condition on the energy functional is needed in our formulation. As an application, we prove the existence of multiple solutions for the following class of elliptic system (S)Δu−u∈[f̲(x,u,v),f¯(x,u,v)]a.e inRN−Δv+v∈[g̲(x,u,v),g¯(x,u,v)]a.e inRN,u,v∈H1(RN), where f and g are measurable functions that satisfy some technical conditions.