Abstract and Applied Analysis
Volume 2012 (2012), Article ID 703596, 15 pages
http://dx.doi.org/10.1155/2012/703596
Research Article

Existence and Multiplicity Results of Homoclinic Solutions for the DNLS Equations with Unbounded Potentials

Defang Ma1,2 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

Received 25 July 2012; Accepted 9 September 2012

Academic Editor: Wenming Zou

Copyright © 2012 Defang Ma 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

A class of difference equations which include discrete nonlinear Schrödinger equations as special cases are considered. New sufficient conditions of the existence and multiplicity results of homoclinic solutions for the difference equations are obtained by making use of the mountain pass theorem and the fountain theorem, respectively. Recent results in the literature are generalized and greatly improved.