Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 179589, 21 pages
doi:10.1155/2008/179589
Research Article
Eventually Periodic Solutions for Difference Equations with Periodic Coefficients and Nonlinear Control Functions
1Department of Mathematics, Yanbian University, Yanji 133002, China
2Department of Mathematics, Tsing Hua University, Hsinchu 30043, Taiwan
Received 13 August 2008; Accepted 24 October 2008
Academic Editor: Guang Zhang
Copyright © 2008 Chengmin Hou and Sui Sun Cheng. 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
For nonlinear difference equations of the form xn=F(n,xn−1,…,xn−m), it is usually difficult to find periodic solutions. In this paper, we consider a class of difference equations of
the form xn=anxn−1+bnf(xn−k), where {an}, {bn} are periodic sequences and f is a nonlinear filtering function, and show how periodic solutions can be constructed. Several examples are also included to illustrate our results.