Table of Contents
International Journal of Partial Differential Equations
Volume 2014, Article ID 640931, 8 pages
http://dx.doi.org/10.1155/2014/640931
Research Article

Existence of the Mild Solution for Impulsive Semilinear Differential Equation

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand 247667, India

Received 26 December 2013; Revised 15 April 2014; Accepted 18 April 2014; Published 18 May 2014

Academic Editor: Yuri N. Skiba

Copyright © 2014 Alka Chadha and Dwijendra N. Pandey. 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

We study the existence of solutions of impulsive semilinear differential equation in a Banach space in which impulsive condition is not instantaneous. We establish the existence of a mild solution by using the Hausdorff measure of noncompactness and a fixed point theorem for the convex power condensing operator.