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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| 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). |
| format | Article |
| id | doaj-art-0a0d816cdd0d4462a8c67147333bb8ea |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| 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 |
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