On the Periodicity of a Difference Equation with Maximum. (1st June 2008) - Gelisken, Ali
Abstract : We investigate the periodic nature of solutions of the max difference equationx n + 1 = max ⁡ { x n, A } / ( x n x n − 1 ), n = 0, 1, …, whereA is a positive real parameter, and the initial conditionsx − 1 = A r − 1 andx 0 = A r 0 such thatr − 1 andr 0 are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005).