Abstract and Applied Analysis
Volume 2008 (2008), Article ID 653243, 8 pages
The Behavior of Positive Solutions of a Nonlinear Second-Order Difference Equation
1Mathematical Institute of the Serbian Academy of Science, Knez Mihailova 35/I, Beograd 11000, Serbia
2Department of Mathematics, Wake Forest University, Winston-Salem, NC 27109, USA
Received 16 August 2007; Accepted 8 December 2007
Academic Editor: Allan C. Peterson
Copyright © 2008 Stevo Stević and Kenneth S. Berenhaut. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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 .