Nonlinear noncoercive Neumann problems

Leszek Gasiński; Liliana  Klimczak; Nikolaos S. Papageorgiou

doi:10.3934/cpaa.2016.15.1107

Article Contents

2016, Volume 15, Issue 4: 1107-1123. Doi: 10.3934/cpaa.2016.15.1107

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Nonlinear noncoercive Neumann problems

1.
Jagiellonian University, Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Kraków
2.
Faculty of Mathematics and Computer Science, ul. Łojasiewicza 6, 30-348 Kraków
3.
Department of Mathematics, National Technical University of Athens, Zografou Campus, Athens 15780

Received: August 2014

Revised: February 2016

Published: July 2016

Abstract / Introduction Related Papers Cited by

Abstract

We consider nonlinear, nonhomogeneous and noncoercive Neumann problems with a Carathéodory reaction which is either $(p-1)$-superlinear near $\pm\infty$ (without satisfying the usual in such cases Ambrosetti-Rabinowitz condition) or $(p-1)$-sublinear near $\pm\infty$. Using variational methods and Morse theory (critical groups) we prove two existence theorems.

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Mathematics Subject Classification: Primary: 35J20; Secondary: 35J60, 58E05.

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