Advances in Difference Equations
Volume 2008 (2008), Article ID 651747, 5 pages
doi:10.1155/2008/651747
Research Article
A Note on the Periodicity of the Lyness Max Equation
Department of Mathematics, Faculty of Education, Selcuk University, 42099 Konya, Turkey
Received 24 October 2007; Accepted 21 December 2007
Academic Editor: Elena Braverman
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
a “max-type” difference equation sometimes referred to as the “Lyness max”
equation. The equation we consider is xn+1=max{xn,A}/xn−1 . where A is a positive real parameter, 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 of Grove and Ladas (2005).