Advances in Difference Equations
Volume 2008 (2008), Article ID 739602, 17 pages
On the Asymptotic Integration of Nonlinear Dynamic Equations
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.
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.