Journal of Applied Mathematics 
Volume 2007 (2007), Article ID 31572, 12 pages
doi:10.1155/2007/31572
Research Article

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

Aneta Sikorska-Nowak

 Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, Poznań 61-614, Poland
Received 9 November 2006; Accepted 26 March 2007

Recommended by Andrei Agrachev

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.