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

In this paper we consider the differential inclusion problem in RN involving the p(x)-Laplacian of the type {−div(|∇u|p(x)−2∇u)+|u|p(x)−2u∈∂F(x,u) inRN,u∈W1,p(x)(RN). We prove the existence of infinitely many radially symmetric solutions of the problem under suitable hypotheses by applying a nonsmooth variational principle due to Marano and Motreanu and the theory of the variable exponent Sobolev spaces.