Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 820629, 11 pages
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

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.


We investigate the periodic nature of solutions of the max difference equation xn+1=max{xn,A}/(xnxn1), n=0,1,, where A is a positive real parameter, and the initial conditions x1=Ar1 and x0=Ar0 such that r1 and r0 are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005).