Advances in Difference Equations
Volume 2011 (2011), Article ID 784161, 17 pages
doi:10.1155/2011/784161
Research Article

Nonlocal Impulsive Cauchy Problems for Evolution Equations

Jin Liang1 and Zhenbin Fan1,2

1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China
2Department of Mathematics, Changshu Institute of Technology, Suzhou, Jiangsu 215500, China

Received 17 October 2010; Accepted 19 November 2010

Academic Editor: Toka Diagana

Copyright © 2011 Jin Liang and Zhenbin Fan. 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

Of concern is the existence of solutions to nonlocal impulsive Cauchy problems for evolution equations. Combining the techniques of operator semigroups, approximate solutions, noncompact measures and the fixed point theory, new existence theorems are obtained, which generalize and improve some previous results since neither the Lipschitz continuity nor compactness assumption on the impulsive functions is required. An application to partial differential equations is also presented.