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

In this paper we consider Neumann-type differential inclusion problems involving the p(x)p(x)-Laplacian of the type {−div(|∇u|p(x)−2∇u)+|u|p(x)−2u∈λ∂F(x,u) in Ω,∂u∂γ=0 on ∂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).