Abstract and Applied Analysis
Volume 2011 (2011), Article ID 815285, 15 pages
http://dx.doi.org/10.1155/2011/815285
Research Article

On the Difference Equation 𝑥 𝑛 + 1 = 𝑥 𝑛 𝑥 𝑛 − 2 − 1

Candace M. Kent,1 Witold Kosmala,2 and Stevo Stević3

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

Received 24 October 2010; Accepted 19 January 2011

Academic Editor: Yong Zhou

Copyright © 2011 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

The long-term behavior of solutions of the following difference equation: 𝑥 𝑛 + 1 = 𝑥 𝑛 𝑥 𝑛 − 2 − 1 , 𝑛 ∈ ℕ 0 , where the initial values 𝑥 − 2 , 𝑥 − 1 , 𝑥 0 are real numbers, is investigated in the paper.