Abstract and Applied Analysis
Volume 2010 (2010), Article ID 469683, 13 pages
doi:10.1155/2010/469683
Research Article

Solutions of the Difference Equation xn+1=xnxn−1−1

Candace M. Kent,1 Witold Kosmala,2 Michael A. Radin,3 and Stevo Stević4

1Department of Mathematics and Applied Mathematics, Virginia Commonwealth University, Richmond, VA 23284, USA
2Department of Mathematical Sciences, Appalachian State University, Boone, NC 28608, USA
3School of Mathematical Sciences, Rochester Institute of Technology, Rochester, NY 14623, USA
4Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia

Received 28 April 2010; Accepted 9 June 2010

Academic Editor: Ağacik Zafer

Copyright © 2010 Candace M. Kent et al. 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.

Abstract

Our goal in this paper is to investigate the long-term behavior of solutions of the following difference equation: xn+1=xnxn−1−1, n=0,1,2,…, where the initial conditions x−1 and x0 are real numbers. We examine the boundedness of solutions, periodicity of solutions, and existence of unbounded solutions and how these behaviors depend on initial conditions.