Abstract and Applied Analysis
Volume 2009 (2009), Article ID 152964, 10 pages
doi:10.1155/2009/152964
Research Article

Global Behavior of the Max-Type Difference Equation xn+1=max⁡{1/xn,An/xn−1}

Taixiang Sun,1 Bin Qin,2 Hongjian Xi,2 and Caihong Han1

1College of Mathematics and Information Science, Guangxi University, Nanning 530004, China
2Department of Mathematics, Guangxi College of Finance and Economics, Nanning 530003, China

Received 4 February 2009; Revised 2 March 2009; Accepted 8 March 2009

Academic Editor: Stevo Stevic

Copyright © 2009 Taixiang Sun 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 study global behavior of the following max-type difference equation xn+1=max⁡{1/xn,An/xn−1}, n=0,1,…, where {An}n=0∞ is a sequence of positive real numbers with 0≤inf⁡An≤sup⁡An<1. The special case when {An}n=0∞ is a periodic sequence with period k and An∈(0,1) for every n≥0 has been completely investigated by Y. Chen. Here we extend his results to the general case.