Multiplicity results for a differential inclusion problem with non-standard growth

In this paper we examine the multiplicity of solutions of a differential inclusion problem involving p(x)p(x)-Laplacian of the type[Pλ]{−Δp(x)u+V(x)|u|p(x)−2u∈∂j1(x,u(x))+λ∂j2(x,u(x)),in Ω,∂u∂n=0,on ∂Ω. By using the nonsmooth version of Ricceri variational principle we get three critical points of the corresponding energy Motreanu–Panagiotopoulos type functional, which are the solutions of (Pλ)(Pλ).