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: | , |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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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| ISSN: | 1085-3375 1687-0409 |