Abstract and Applied Analysis
Volume 2010 (2010), Article ID 237129, 6 pages
doi:10.1155/2010/237129
Research Article

Global Behavior of the Difference Equation xn+1=(p+xn-1)/(qxn+xn-1)

Taixiang Sun,1 Hongjian Xi,2 Hui Wu,1 and Caihong Han1

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

Received 31 March 2010; Revised 17 April 2010; Accepted 30 April 2010

Academic Editor: Stevo Stević

Copyright © 2010 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.

Abstract

We study the following difference equation xn+1=(p+xn-1)/(qxn+xn-1), n=0,1,…, where p,q∈(0,+∞) and the initial conditions x-1,x0∈(0,+∞). We show that every positive solution of the above equation either converges to a finite limit or to a two cycle, which confirms that the Conjecture 6.10.4 proposed by Kulenović and Ladas (2002) is true.