On the Periodicity of a Difference Equation with Maximum

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).