Abstract and Applied Analysis
Volume 2011 (2011), Article ID 436852, 15 pages
http://dx.doi.org/10.1155/2011/436852
Research Article

On a Class of Nonautonomous Max-Type Difference Equations

Wanping Liu,1 Xiaofan Yang,1 and Stevo Stevic2

1College of Computer Science, Chongqing University, Chongqing 400044, China
2Mathematical Institute of the Serbian Academy of Sciences, Knez Mihailova 36/III, 11000 Beograd, Serbia

Received 15 February 2011; Accepted 14 June 2011

Academic Editor: Gaston Mandata N'Guerekata

Copyright © 2011 Wanping Liu 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

This paper addresses the max-type difference equation xn=max{fn/xn−kα,B/xn−mβ}, n∈ℕ0, where k,m∈ℕ, B>0, and (fn)n∈ℕ0 is a positive sequence with a finite limit. We prove that every positive solution to the equation converges to max{(limn→∞fn)1/(α+1),B1/(β+1)} under some conditions. Explicit positive solutions to two particular cases are also presented.