Abstract and Applied Analysis

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

Cristóbal González and Antonio Jiménez-Melado

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Abstract

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 ( γ 1 ( s ) ) , , y ( γ N ( s ) )) d s , 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 ( γ 1 ( s ) ) , , y ( γ N ( s ) )) d s , 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 ( γ 1 ( t ) ) , , y ( γ N ( t ) ) ) = 0 , with the same asymptotic behavior at as ω ( t ) .

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 957696, 7 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393449713

Digital Object Identifier
doi:10.1155/2013/957696

Mathematical Reviews number (MathSciNet)
MR3147793

Zentralblatt MATH identifier
07095536

Citation

González, Cristóbal; Jiménez-Melado, Antonio. Asymptotic Behavior of Solutions to a Vector Integral Equation with Deviating Arguments. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 957696, 7 pages. doi:10.1155/2013/957696. https://projecteuclid.org/euclid.aaa/1393449713


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