Existence of solutions of the Neumann problem for a class of equations involving the p-Laplacian in weighted Sobolev spaces

Abstract

In this paper we consider the Neumann problem involving the p-Laplacian of the type −div w 1 (x)| ∇u | p−2 ∇u + w 0 (x)| u | p−2 u = α(x)f (u) + β(x)g(u) in Ω, ∂u ∂γ = 0 on ∂Ω. We prove the existence of weak solutions for this problem under weak hypotheses by applying a variational principle due to B.Ricceri and the theory of the weighted Sobolev spaces. Our results are an improvement and generalization of the relative results obtained by [3] for the p-Laplacian case.