Discrete Dynamics in Nature and Society
Volume 2012 (2012), Article ID 930410, 11 pages
http://dx.doi.org/10.1155/2012/930410
Research Article

Global Attractivity of a Higher-Order Difference Equation

R. Abo-Zeid

Department of Mathematics, College of Science & Arts-Rabigh, King Abdulaziz University, Rabigh 21911, Saudi Arabia

Received 7 May 2012; Accepted 8 July 2012

Academic Editor: M. De la Sen

Copyright © 2012 R. Abo-Zeid. 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 aim of this work is to investigate the global stability, periodic nature, oscillation, and the boundedness of all admissible solutions of the difference equation 𝑥 𝑛 + 1 = 𝐴 𝑥 𝑛 − 2 𝑟 − 1 ∏ / ( 𝐵 − 𝐶 𝑘 𝑖 = 𝑙 𝑥 𝑛 − 2 𝑖 ) , 𝑛 = 0 , 1 , 2 , … where 𝐴 , 𝐵 , 𝐶 are positive real numbers and 𝑙 , 𝑟 , 𝑘 are nonnegative integers, such that 𝑙 ≤ 𝑘 .