Advances in Difference Equations
Volume 2010 (2010), Article ID 970720, 14 pages
Research Article

Dynamics of a Rational Difference Equation

1Department of Mathematics, Hexi University, Zhangye, Gansu 734000, China
2School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China
3Department of Mathematics, Tianshui Normal University, Tianshui, Gansu 741001, China

Received 5 November 2009; Accepted 5 April 2010

Academic Editor: Martin Bohner

Copyright © 2010 Xiu-Mei Jia 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.


The main goal of the paper is to investigate boundedness, invariant intervals, semicycles, and global attractivity of all nonnegative solutions of the equation xn+1=(α+βxn+γxn-k)/(1+xn-k), n0, where the parameters α,β,γ[0,), k2 is an integer, and the initial conditions x-k,,x0[0,). It is shown that the unique positive equilibrium of the equation is globally asymptotically stable under the condition β1. The result partially solves the open problem proposed by Kulenović and Ladas in work (2002).