Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 20652, 7 pages
doi:10.1155/DDNS/2006/20652

On boundedness of the solutions of the difference equation xn+1=xn−1/(p+xn)

Taixiang Sun1 , Hongjian Xi2 and Hui Wu1

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

Abstract

We study the difference equation xn+1=xn−1/(p+xn), n=0,1,…, where initial values x−1,x0∈(0,+∞) and 0<p<1, and obtain the set of all initial values (x−1,x0)∈(0,+∞)×(0,+∞) such that the positive solution {xn}n=−1∞ is bounded. This answers the Open Problem 2 proposed by Kulenović and Ladas.