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Abstract and Applied Analysis
Volume 2014, Article ID 705893, 5 pages
Research Article

Global Behavior of the Difference Equation

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

Received 17 November 2013; Accepted 23 December 2013; Published 3 February 2014

Academic Editor: Tongxing Li

Copyright © 2014 Hongjian Xi 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.


We consider the following difference equation , where initial values and is a strictly decreasing continuous surjective function. We show the following. (1) Every positive solution of this equation converges to or for some . (2) Assume . Then the set of initial conditions such that the positive solutions of this equation converge to or is a unique strictly increasing continuous function or an empty set.