p-Laplace equations with singular terms and p-superlinear perturbations

Abstract

We consider a nonlinear parametric Neumann problem driven by the p-Laplacian with a singular term and a Caratheodory perturbation whose primitive is p- superlinear near +∞ but needs not satisfy the Ambrosetti-Rabinowitz condition. We show that when the parameter λ>0 is small, the problem has at least two nontrivial positive smooth solutions. Our method of proof uses an approximation of the original problem, which we solve using variational techniques and then pass to the limit.