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 Sun,1 Hongjian Xi,2 and Hui Wu1

 1Department of Mathematics, College of Mathematics and Information Science, Guangxi University, Nanning 530004, Guangxi, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning 530003, Guangxi, China
Received 29 April 2006; Revised 4 July 2006; Accepted 5 July 2006

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.