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

In this paper, we propose the study of an integral equation, with deviating arguments, of the type y(t)=ω(t)-∫0∞‍f(t,s,y(γ1(s)),…,y(γN(s)))ds,t≥0, in the context of Banach spaces, with the intention of giving sufficient conditions that ensure the existence of solutions with the same asymptotic behav...

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Main Authors: Cristóbal González, Antonio Jiménez-Melado
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/957696
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author Cristóbal González
Antonio Jiménez-Melado
author_facet Cristóbal González
Antonio Jiménez-Melado
author_sort Cristóbal González
collection DOAJ
description In this paper, we propose the study of an integral equation, with deviating arguments, of the type y(t)=ω(t)-∫0∞‍f(t,s,y(γ1(s)),…,y(γN(s)))ds,t≥0, 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 ω(t). A similar equation, but requiring a little less restrictive hypotheses, is y(t)=ω(t)-∫0∞‍q(t,s)F(s,y(γ1(s)),…,y(γN(s)))ds,t≥0. In the case of q(t,s)=(t-s)+, its solutions with asymptotic behavior given by ω(t) yield solutions of the second order nonlinear abstract differential equation y''(t)-ω''(t)+F(t,y(γ1(t)),…,y(γN(t)))=0, with the same asymptotic behavior at ∞ as ω(t).
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publishDate 2013-01-01
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spelling doaj-art-0a0d816cdd0d4462a8c67147333bb8ea2025-02-03T05:57:07ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/957696957696Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating ArgumentsCristóbal González0Antonio Jiménez-Melado1Departamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, SpainDepartamento de Análisis Matemático, Facultad de Ciencias, Universidad de Málaga, 29071 Málaga, SpainIn this paper, we propose the study of an integral equation, with deviating arguments, of the type y(t)=ω(t)-∫0∞‍f(t,s,y(γ1(s)),…,y(γN(s)))ds,t≥0, 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 ω(t). A similar equation, but requiring a little less restrictive hypotheses, is y(t)=ω(t)-∫0∞‍q(t,s)F(s,y(γ1(s)),…,y(γN(s)))ds,t≥0. In the case of q(t,s)=(t-s)+, its solutions with asymptotic behavior given by ω(t) yield solutions of the second order nonlinear abstract differential equation y''(t)-ω''(t)+F(t,y(γ1(t)),…,y(γN(t)))=0, with the same asymptotic behavior at ∞ as ω(t).http://dx.doi.org/10.1155/2013/957696
spellingShingle Cristóbal González
Antonio Jiménez-Melado
Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments
Abstract and Applied Analysis
title Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments
title_full Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments
title_fullStr Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments
title_full_unstemmed Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments
title_short Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments
title_sort asymptotic behavior of solutions to a vector integral equation with deviating arguments
url http://dx.doi.org/10.1155/2013/957696
work_keys_str_mv AT cristobalgonzalez asymptoticbehaviorofsolutionstoavectorintegralequationwithdeviatingarguments
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