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Journal of Applied Mathematics
Volume 2007, Article ID 31572, 12 pages
Research Article

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

Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, Poznań 61-614, Poland

Received 9 November 2006; Accepted 26 March 2007

Academic Editor: Andrei Agrachev

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.


We prove existence theorems for the integrodifferential equation x'(t)=f(t,x(t),0tk(t,s, x(s))ds), x(0)=x0, tIa=[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.