POSITIVE SOLUTIONS FOR PERTURBATIONS OF THE EIGENVALUE PROBLEM FOR

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. 1