Advances in Difference Equations
Volume 2008 (2008), Article ID 651747, 5 pages
doi:10.1155/2008/651747
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
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).