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
E. Akin et al., "On the Asymptotic Integration of Nonlinear Dynamic Equations," Advances in Difference Equations, vol. 2008, Hindawi Publishing Corporation, Jan 2008.
The definitive version is available at http://dx.doi.org/10.1155/2008/739602
Mathematics and Statistics
National Science Foundation (U.S.)
Keywords and Phrases
Banach Fixed Point Theorem; Boyd and Wong Fixed Point Theorem; Leray-Schauder Nonlinear Alternative; Schauder Fixed Point Theorem
Article - Journal
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