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Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 90625, 12 pages

On the global behavior of the nonlinear difference equation xn+1=f(pn,xnm,xnt(k+1)+1)

1College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China

Received 7 February 2006; Accepted 5 April 2006

Copyright © 2006 Taixiang Sun and Hongjian Xi. 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.


We consider the following nonlinear difference equation: xn+1=f(pn,xnm,xnt(k+1)+1), n=0,1,2,, where m{0,1,2,} and k,t{1,2,} with 0m<t(k+1)1, the initial values xt(k+1)+1,xt(k+1)+2,,x0(0,+), and {pn}n=0 is a positive sequence of the period k+1. We give sufficient conditions under which every positive solution of this equation tends to the period k+1 solution.