Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 820629, 11 pages
doi:10.1155/2008/820629
Research Article
On the Periodicity of a Difference Equation with Maximum
Department of Mathematics, Education Faculty, Selcuk University, 42099 KONYA, Turkey
Received 20 January 2008; Revised 8 April 2008; Accepted 18 May 2008
Academic Editor: Yong Zhou
Copyright © 2008 Ali Gelisken 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 investigate the periodic nature of solutions of the max difference equation xn+1=max{xn,A}/(xnxn−1), n=0,1,…, where A is a positive real parameter, and the initial conditions x−1=Ar−1 and x0=Ar0 such that r−1 and r0 are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005).