Discrete Dynamics in Nature and Society
Volume 2008 (2008), Article ID 820629, 11 pages
doi:10.1155/2008/820629
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
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).