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

On boundedness of the solutions of the difference equation xn+1=xn1/(p+xn)

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

Received 29 April 2006; Revised 4 July 2006; Accepted 5 July 2006

Copyright © 2006 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 difference equation xn+1=xn1/(p+xn), n=0,1,, where initial values x1,x0(0,+) and 0<p<1, and obtain the set of all initial values (x1,x0)(0,+)×(0,+) such that the positive solution {xn}n=1 is bounded. This answers the Open Problem 2 proposed by Kulenović and Ladas.