Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 179589, 21 pages
doi:10.1155/2008/179589
Eventually periodic solutions for difference equations with periodic coefficients and nonlinear control functions
Chengmin Hou1
and Sui Sun Cheng2
1Department of Mathematics, Yanbian University, Yanji 133002, China
2Department of Mathematics, Tsing Hua University, Hsinchu 30043, Taiwan
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.