Multiple Solutions for a Class of Differential Inclusion System Involving the (p(x),q(x))-Laplacian

Abstract

We consider a differential inclusion system involving the (p(x),q(x))-Laplacian with Dirichlet boundary condition on a bounded domain and obtain two nontrivial solutions under appropriate hypotheses. Our approach is variational and it is based on the nonsmooth critical point theory for locally Lipschitz functions.