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Abstract:In this work we study the asymptotic stability of the nonnegative equilibrium points of the difference equation

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 x n 1 max{x n , A}/x n−1 . where A is a positive real parameter, x − 1 A r −1 , and x 0 A r 0 such that r −1 and r 0 are positive rational numbers. The results in this paper answer the Open Problem of Grove and Ladas 2005 .

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