Advances in Difference Equations
Volume 2009 (2009), Article ID 235691, 13 pages
doi:10.1155/2009/235691
Research Article

Dynamics for Nonlinear Difference Equation xn+1=(αxn−k)/(β+γxn−lp)

Dongmei Chen,1 Xianyi Li,1 and Yanqin Wang2

1College of Mathematics and Computational Science, Shenzhen University, Shenzhen, Guangdong 518060, China
2School of Physics & Mathematics, Jiangsu Polytechnic University, Changzhou, 213164 Jiangsu, China

Received 19 April 2009; Revised 19 August 2009; Accepted 9 October 2009

Academic Editor: Mariella Cecchi

Copyright © 2009 Dongmei Chen 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

We mainly study the global behavior of the nonlinear difference equation in the title, that is, the global asymptotical stability of zero equilibrium, the existence of unbounded solutions, the existence of period two solutions, the existence of oscillatory solutions, the existence, and asymptotic behavior of non-oscillatory solutions of the equation. Our results extend and generalize the known ones.