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Abstract and Applied Analysis
Volume 2012 (2012), Article ID 647103, 15 pages
http://dx.doi.org/10.1155/2012/647103
Research Article

Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial Conditions

1Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago 9160000, Chile
2Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, Santiago 7810000, Chile

Received 26 October 2012; Accepted 14 December 2012

Academic Editor: Józef Banaś

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.