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Abstract and Applied Analysis
Volume 2013, Article ID 957696, 7 pages
http://dx.doi.org/10.1155/2013/957696
Research Article

Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments

Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, Spain

Received 31 July 2013; Accepted 5 November 2013

Academic Editor: István Györi

Copyright © 2013 Cristóbal González and Antonio Jiménez-Melado. 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

In this paper, we propose the study of an integral equation, with deviating arguments, of the type in the context of Banach spaces, with the intention of giving sufficient conditions that ensure the existence of solutions with the same asymptotic behavior at as . A similar equation, but requiring a little less restrictive hypotheses, is In the case of , its solutions with asymptotic behavior given by yield solutions of the second order nonlinear abstract differential equation with the same asymptotic behavior at as .