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Advances in Mathematical Physics
Volume 2013 (2013), Article ID 823535, 6 pages
http://dx.doi.org/10.1155/2013/823535
Research Article

Mild Solutions of Neutral Semilinear Stochastic Functional Dynamic Systems with Local Non-Lipschitz Coefficients

School of Statistics and Mathematics, Zhongnan University of Economics and Law, Wuhan 430073, China

Received 12 March 2013; Accepted 27 June 2013

Academic Editor: H. Srivastava

Copyright © 2013 Feng Jiang. 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

Semilinear stochastic dynamic systems in a separable Hilbert space often model some evolution phenomena arising in physics and engineering. In this paper, we study the existence and uniqueness of mild solutions to neutral semilinear stochastic functional dynamic systems under local non-Lipschitz conditions on the coefficients by means of the stopping time technique. We especially generalize and improve the results that appeared in Govinadan (2005), Bao and Hou (2010), and Jiang and Shen (2011).