POSITIVE SOLUTIONS FOR PERTURBATIONSOF THE EIGENVALUE PROBLEM FOR THE ROBIN p-LAPLACIAN

摘要

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.