This paper studies the boundedness, global asymptotic stability, and periodicity of positive solutions of the equation , , where . It is shown that if and are nondecreasing, then for every solution of the equation the subsequences and are eventually monotone. For the case when and satisfies the conditions , is nondecreasing, and is increasing, we prove that every prime periodic solution of the equation has period equal to one or two. We also investigate the global periodicity of the equation, showing that if all solutions of the equation are periodic with period three, then and , for some positive and .
"The Behavior of Positive Solutions of a Nonlinear Second-Order Difference Equation." Abstr. Appl. Anal. 2008 1 - 8, 2008. https://doi.org/10.1155/2008/653243