We investigate asymptotic behavior and periodic nature of positive solutions of the difference equation , where and . We prove that every positive solution of this difference equation approaches or is eventually periodic with period 2.
We investigate the periodic nature of solutions of the max difference equationxn+1=max{xn,A}/(xnxn−1),n=0,1,…, whereAis a positive real parameter, and the initial conditionsx−1=Ar−1andx0=Ar0such thatr−1andr0are positive rational numbers. The results in this paper answer the Open Problem 6.2 posed by Grove and Ladas (2005).
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