Discrete Dynamics in Nature and Society
Volume 2010 (2010), Article ID 610467, 17 pages
doi:10.1155/2010/610467
Research Article

Boundedness and Global Attractivity of a Higher-Order Nonlinear Difference Equation

Xiu-Mei Jia1,2 and Wan-Tong Li2

1Department of Mathematics, Hexi University, Zhangye, Gansu 734000, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China

Received 5 November 2009; Accepted 4 February 2010

Academic Editor: Guang Zhang

Copyright © 2010 Xiu-Mei Jia and Wan-Tong Li. 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

We investigate the local stability, prime period-two solutions, boundedness, invariant intervals, and global attractivity of all positive solutions of the following difference equation: yn+1=(r+pyn+yn−k)/(qyn+yn−k), n∈ℕ0, where the parameters p,q,r∈(0,∞),k∈{1,2,3,…} and the initial conditions y−k,…,y0∈(0,∞). We show that the unique positive equilibrium of this equation is a global attractor under certain conditions.