Advances in Difference Equations
Volume 2011 (2011), Article ID 634701, 18 pages
Research Article

Impulsive Integrodifferential Equations Involving Nonlocal Initial Conditions

Department of Mathematics, NanChang University, NanChang, JiangXi 330031, China

Received 23 November 2010; Revised 22 February 2011; Accepted 7 March 2011

Academic Editor: Jin Liang

Copyright © 2011 Rong-Nian Wang and Jun Xia. 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.


We focus on a Cauchy problem for impulsive integrodifferential equations involving nonlocal initial conditions, where the linear part is a generator of a solution operator on a complex Banach space. A suitable mild solution for the Cauchy problem is introduced. The existence and uniqueness of mild solutions for the Cauchy problem, under various criterions, are proved. In the last part of the paper, we construct an example to illustrate the feasibility of our results.