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Discrete Dynamics in Nature and Society
Volume 2006 (2006), Article ID 47156, 10 pages
http://dx.doi.org/10.1155/DDNS/2006/47156

Asymptotic behavior of a class of nonlinear difference equations

Mathematical Institute, Serbian Academy of Science and Arts, Knez Mihailova 35/I, Beograd 11000, Serbia

Received 7 April 2006; Accepted 28 May 2006

Copyright © 2006 Stevo Stević. 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

Motivated by some results of L. Berg (2002), in this paper we find the second member in the asymptotic development of some of the positive solutions of a class of difference equations of second and third orders. The main result in this paper partially solves an open problem by S. Stević (2003), and it is applied to some classes of mathematical biology models, for example, generalized Beverton-Holt stock recruitment model, flour beetle population model, mosquito population equations, and discrete delay logistic difference equation.