Positive solutions for perturbations of the eigenvalue problem for the robin p-Laplacian

Abstract

We study perturbations of the eigenvalue problem for the Robin p-Laplacian. First we consider the case of a (p - 1)-sublinear perturbation and prove existence, nonexistence and uniqueness of positive solutions. Then we deal with the case of a (p - 1)-superlinear perturbation which need not satisfy the Ambrosetti-Rabinowitz condition and prove a multiplicity result for positive solutions. Our approach uses variational methods together with suitable truncation and perturbation techniques.