About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 707686, 8 pages
http://dx.doi.org/10.1155/2013/707686
Research Article

Estimate of Number of Periodic Solutions of Second-Order Asymptotically Linear Difference System

School of Science, Jimei University, Xiamen 361021, China

Received 1 April 2013; Accepted 5 June 2013

Academic Editor: Zidong Wang

Copyright © 2013 Honghua Bin and Zhenkun Huang. 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 investigate the number of periodic solutions of second-order asymptotically linear difference system. The main tools are Morse theory and twist number, and the discussion in this paper is divided into three cases. As the system is resonant at infinity, we use perturbation method to study the compactness condition of functional. We obtain some new results concerning the lower bounds of the nonconstant periodic solutions for discrete system.