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Journal of Function Spaces and Applications
Volume 2013, Article ID 451252, 11 pages
http://dx.doi.org/10.1155/2013/451252
Research Article

Existence of Solutions in Some Interpolation Spaces for a Class of Semilinear Evolution Equations with Nonlocal Initial Conditions

1Department of Applied Mathematics, I-Shou University, Ta-Hsu, Kaohsiung 84008, Taiwan
2Department of Information Management, Yang Ze University, Jhongli, Taoyuan 32097, Taiwan

Received 29 May 2013; Accepted 7 July 2013

Academic Editor: J. Liang

Copyright © 2013 Jung-Chan Chang and Hsiang Liu. 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

This paper is concerned with the existence of mild and strong solutions for a class of semilinear evolution equations with nonlocal initial conditions. The linear part is assumed to be a (not necessarily densely defined) sectorial operator in a Banach space . Considering the equations in the norm of some interpolation spaces between and the domain of the linear part, we generalize the recent conclusions on this topic. The obtained results will be applied to a class of semilinear functional partial differential equations with nonlocal conditions.