Journal of Applied Mathematics
Volume 2007 (2007), Article ID 31572, 12 pages
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 , , , , where are functions with values in a Banach space and the integral is taken in the sense of HL.
Additionally, the functions and satisfy certain boundary conditions expressed in terms of the measure