On a Neumann problem with p-Laplacian and noncoercive resonant nonlinearity

Salvatore A. Marano and Nikolaos S. Papageorgiou

Vol. 253 (2011), No. 1, 103–123

DOI: 10.2140/pjm.2011.253.103

Abstract

Using variational techniques and Morse theory, we establish three existence results for a Neumann boundary-value problem with p-Laplacian and Carathéodory reaction term, which can be (p−1)-asymptotically linear or sublinear at infinity. The hypotheses taken on permit resonance and make the corresponding energy functional noncoercive.

Keywords

p-Laplacian, Neumann problem, noncoercive resonant nonlinearity

Mathematical Subject Classification 2000

Primary: 35J25, 35J70, 58E05

Milestones

Received: 17 March 2010

Accepted: 28 June 2011

Published: 28 November 2011