Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

Sikorska-Nowak, Aneta

doi:https://doi.org/10.1155/2007/31572

Journal of Applied Mathematics

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Research Article | Open Access

Volume 2007 | Article ID 031572 | https://doi.org/10.1155/2007/31572

Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

Aneta Sikorska-Nowak¹

Academic Editor: Andrei Agrachev

Received09 Nov 2006

Accepted26 Mar 2007

Published27 Jun 2007

Abstract

We prove existence theorems for the integrodifferential equation x'(t)=f(t,x(t),∫0tk(t,s, x(s))ds), x(0)=x0, t∈Ia=[0,a], a>0, where f,k,x are functions with values in a Banach space E and the integral is taken in the sense of HL. Additionally, the functions f and k satisfy certain boundary conditions expressed in terms of the measure of noncompactness.

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Copyright © 2007 Aneta Sikorska-Nowak. 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.

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