Positive solutions for perturbations of the eigenvalue problem for the Robin p-Laplacian
Νικόλαος Παπαγεωργίου, Vicenţiu D. Rădulescu · Annales Academiae Scientiarum Fennicae Mathematica · 2015
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.