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 ) -Laplacian of the type [ P λ ] { − Δ p ( x ) u + V ( x ) | u | p ( x ) − 2 u ∈ ∂ j 1 ( x , u ( x ) ) + λ ∂ j 2 ( 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 ( P λ ) .