This paper shows the existence and multiplicity of nontrivial solutions of the p-Laplacian problem -Δpu=1/σ(∂F(x,u)/∂u)+λa(x)|u|q-2u for x∈Ω with zero Dirichlet boundary conditions, where Ω is a bounded open set in ℝn, 1<q<p<σ<p*(p*=np/(n-p) if p<n, p*=∞ if p≥n), λ∈ℝ∖{0}, a is a smooth function which may change sign in Ω̅,, and F∈C1(Ω̅ × ℝ,ℝ). The method is based on Nehari results on three submanifolds of the space W01,p(Ω).