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 $\left(p\left(x\right),q\left(x\right)\right)$-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.