International Journal of Stochastic Analysis
Volume 2011 (2011), Article ID 784638, 17 pages
http://dx.doi.org/10.1155/2011/784638
Research Article

Existence Results for Stochastic Semilinear Differential Inclusions with Nonlocal Conditions

A. Vinodkumar1 and A. Boucherif2

1Department of Mathematics and Computer Applications, PSG College of Technology, Coimbatore, Tamil Nadu 641 004, India
2Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, P.O. Box 5046, Dhabran 31261, Saudi Arabia

Received 31 May 2011; Accepted 6 October 2011

Academic Editor: Jiongmin Yong

Copyright © 2011 A. Vinodkumar and A. Boucherif. 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 discuss existence results of mild solutions for stochastic differential inclusions subject to nonlocal conditions. We provide sufficient conditions in order to obtain a priori bounds on possible solutions of a one-parameter family of problems related to the original one. We, then, rely on fixed point theorems for multivalued operators to prove our main results.