Document Type

Article

Publication Date

2017

Publication Title

Discrete and Continuous Dynamical Systems, Series A

DOI

10.3934/dcds.2017095

ISSN

1553-5231

Abstract

We present here, in the system setting, a new set of growth conditions under which we manage to use a novel method to verify the Cerami compactness condition. By localization argument, decomposition technique and variational methods, we are able to show the existence of multiple solutions with constant sign for the problem without the well-known Ambrosetti--Rabinowitz type growth condition. More precisely, we manage to show that the problem admits four, six and infinitely many solutions respectively.

Comments

This version of the paper was obtained from arXIV.org. In order for the work to be deposited in arXIV.org, it must be available under the Creative Commons Attribution license, Creative Commons Attribution-Noncommercial-ShareAlike license, or Create Commons Public Domain Declaration. The publisher's final edited version of this article is available at Discrete and Continuous Dynamical Systems, Series A.

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Mathematics Commons

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