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The Scientific World Journal
Volume 2014, Article ID 276372, 6 pages
http://dx.doi.org/10.1155/2014/276372
Research Article

Infinitely Many Homoclinic Solutions for Second Order Nonlinear Difference Equations with -Laplacian

1Department of Applied Mathematics, Yuncheng University, Yuncheng 044000, China
2School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China

Received 12 March 2014; Accepted 18 April 2014; Published 14 May 2014

Academic Editor: Maoan Han

Copyright © 2014 Guowei Sun and Ali Mai. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We employ Nehari manifold methods and critical point theory to study the existence of nontrivial homoclinic solutions of discrete -Laplacian equations with a coercive weight function and superlinear nonlinearity. Without assuming the classical Ambrosetti-Rabinowitz condition and without any periodicity assumptions, we prove the existence and multiplicity results of the equations.