Advances in Difference Equations
Volume 2008 (2008), Article ID 739602, 17 pages
doi:10.1155/2008/739602
Research Article

On the Asymptotic Integration of Nonlinear Dynamic Equations

Elvan Akın-Bohner,1 Martin Bohner,1 Smaïl Djebali,2 and Toufik Moussaoui2

1Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, MO 65409-0020, USA
2Départment de Mathématiques, École Normale Supérieure, P.O. Box 92, 16050 Kouba, Algiers, Algeria

Received 25 June 2007; Revised 12 November 2007; Accepted 29 January 2008

Academic Editor: Ondřej Došlý

Copyright © 2008 Elvan Akın-Bohner 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

The purpose of this paper is to study the existence and asymptotic behavior of solutions to a class of second-order nonlinear dynamic equations on unbounded time scales. Four different results are obtained by using the Banach fixed point theorem, the Boyd and Wong fixed point theorem, the Leray-Schauder nonlinear alternative, and the Schauder fixed point theorem. For each theorem, an illustrative example is presented. The results provide unification and some extensions in the time scale setup of the theory of asymptotic integration of nonlinear equations both in the continuous and discrete cases.