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Journal of Applied Mathematics
Volume 2014, Article ID 749678, 8 pages
http://dx.doi.org/10.1155/2014/749678
Research Article

Homoclinic Solutions for a Class of Nonlinear Difference Equations

Ali Mai1,2,3 and Zhan Zhou1,2

1School of Mathematics and Information Science, Guangzhou University, Guangdong, Guangzhou 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangdong, Guangzhou 510006, China
3Department of Applied Mathematics, Yuncheng University, Shanxi, Yuncheng 044000, China

Received 11 November 2013; Accepted 6 January 2014; Published 20 February 2014

Academic Editor: Renat Zhdanov

Copyright © 2014 Ali Mai and Zhan Zhou. 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 prove the existence of homoclinic solutions of a class of nonlinear difference equations with superlinear nonlinearity by using the generalized Nehari manifold approach. For the case where the nonlinearity is odd, we obtain infinitely many homoclinic solutions of the equations. Recent results in the literature are generalized and improved.