Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 40, 2015, 255-277

POSITIVE SOLUTIONS FOR PERTURBATIONS OF THE EIGENVALUE PROBLEM FOR THE ROBIN p-LAPLACIAN

Nikolaos S. Papageorgiou and Vicentiu D. Radulescu

National Technical University, Department of Mathematics
Zografou Campus, Athens 15780, Greece; npapg 'at' math.ntua.gr

King Abdulaziz University, Faculty of Science, Department of Mathematics
Jeddah, Saudi Arabia; vicentiu.radulescu 'at' math.cnrs.fr

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.

2010 Mathematics Subject Classification: Primary 35J66, 35J70, 35J92.

Key words: Robin boundary condition, nonlinear regularity, (p – 1)-sublinear and (p – 1)-superlinear perturbation, maximum principle.

Reference to this article: N. S. Papageorgiou and V. D. Radulescu: Positive solutions for perturbations of the eigenvalue problem for the Robin p-Laplacian. Ann. Acad. Sci. Fenn. Math. 40 (2015), 255-277.

Full document as PDF file

doi:10.5186/aasfm.2015.4011