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

Ali Gelisken, Cengiz Cinar, and Ibrahim Yalcinkaya

 Department of Mathematics, Education Faculty, Selcuk University, 42099 KONYA, Turkey
Received 20 January 2008; Revised 8 April 2008; Accepted 18 May 2008

Recommended by Yong Zhou

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).