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

Ali Gelisken, Cengiz Cinar, and Ramazan Karatas

 Department of Mathematics, Faculty of Education, Selcuk University, 42099 Konya, Turkey
Received 24 October 2007; Accepted 21 December 2007

Recommended by Elena Braverman

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).