Existence of infinitely many solutions for a Neumann problem involving the p(x)-Laplacian

In this paper we consider the Neumann problem involving the 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 the problem under weaker hypotheses by applying a variational principle due to B. Ricceri and the theory of the variable exponent Sobolev spaces. Our results are an improvement and generalization of the relative results obtained by B. Ricceri for the p-Laplacian case. © 2006 Elsevier Inc. All rights reserved