Three solutions for a differential inclusion problem involving the p(x)p(x)-Laplacian

In this paper we consider differential inclusion problem involving the p(x)p(x)-Laplacian of the type {−div(|∇u|p(x)−2∇u)∈λ∂F(x,u) in Ω,u=0on ∂Ω. Applying a version of the non-smooth three-critical-points theorem we obtain the existence of three solutions of the problem in W01,p(x)(Ω).