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)p(x)-Laplacian of the type {− div(|∇u|p(x)−2∇u)+λ(x)|u|p(x)−2u∈∂F(x,u)+∂G(x,u)in Ω,∂u∂γ=0 on ∂Ω. We prove the existence of infinitely many solutions of this problem under suitable hypotheses by applying a non-smooth Ricceri-type variational principle and the theory of the variable exponent Sobolev spaces.