Copyright © 2012 Carlos Lizama and Juan C. Pozo. 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.

Abstract

Using Hausdorff measure of noncompactness and a fixed-point argument we prove the existence of mild solutions for the semilinear integrodifferential equation subject to nonlocal initial conditions , , , where , and for every the maps are linear closed operators defined in a Banach space . We assume further that for every , and the functions and are -valued functions which satisfy appropriate conditions.