Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 917560, 8 pages
Research Article

Existence of Monotone Solutions of a Difference Equation

Taixiang Sun,1 Hongjian Xi,1,2 and Weizhen Quan1,3

1Department of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning, Guangxi 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning, Guangxi 530003, China
3Department of Mathematics, Zhanjiang Normal College, Zhanjiang, Guangdong 524048, China

Received 5 February 2008; Revised 31 July 2008; Accepted 9 September 2008

Academic Editor: Stevo Stevic

Copyright © 2008 Taixiang Sun et al. 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 nonlinear difference equation xn+1=f(xnk,xnk+1,,xn), n=0,1,, where k{1,2,} and the initial values xk,xk+1,,x0(0,+). We give sufficient conditions under which this equation has monotone positive solutions which converge to the equilibrium, extending and including in this way some results of the literature.