Infinitely many solutions for a Neumann-type differential inclusion problem involving the p(x)-Laplacian

In this paper we consider a differential inclusion problem involving the p(x)-Laplacian of the type {-div(vertical bar del u vertical bar(p(x)-2)del u) + lambda(x)vertical bar u vertical bar(p(x)-2)u is an element of partial derivative F(x,u) + partial derivative G(x,u) in Omega, partial derivative u/partial derivative gamma = 0 on partial derivative Omega. We prove the existence of infinitely many solutions of this problem under suitable hypotheses by applying a non-smooth Ricceritype variational principle and the theory of the variable exponent Sobolev spaces. (C) 2008 Elsevier Ltd. All rights reserved.