Abstract and Applied Analysis
Volume 2013 (2013), Article ID 842594, 6 pages
http://dx.doi.org/10.1155/2013/842594
Research Article

Standing Wave Solutions for the Discrete Coupled Nonlinear Schrödinger Equations with Unbounded Potentials

Meihua Huang1,2 and Zhan Zhou1,2

1School of Mathematics and Information Science, Guangzhou University, Guangzhou, Guangdong 510006, China
2Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, Guangdong 510006, China

Received 18 January 2013; Accepted 25 February 2013

Academic Editor: Chuangxia Huang

Copyright © 2013 Meihua Huang 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 demonstrate the existence of standing wave solutions of the discrete coupled nonlinear Schrödinger equations with unbounded potentials by using the Nehari manifold approach and the compact embedding theorem. Sufficient conditions are established to show that the standing wave solutions have both of the components not identically zero.