Journal of Applied Mathematics
Volume 2012 (2012), Article ID 720139, 21 pages
http://dx.doi.org/10.1155/2012/720139
Research Article

Homoclinic Orbits for a Class of Noncoercive Discrete Hamiltonian Systems

Long Yuhua1,2

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

Received 9 June 2012; Accepted 8 August 2012

Academic Editor: Wan-Tong Li

Copyright © 2012 Long Yuhua. 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 first-order noncoercive discrete Hamiltonian systems are considered. Based on a generalized mountain pass theorem, some existence results of homoclinic orbits are obtained when the discrete Hamiltonian system is not periodical and need not satisfy the global Ambrosetti-Rabinowitz condition.