Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article The Existence and Exponential Stability for Random Impulsive Integrodifferential Equations of Neutral Type | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 54o365 18 pages doi 2010 540365 Research Article The Existence and Exponential Stability for Random Impulsive Integrodifferential Equations of Neutral Type Huabin Chen Xiaozhi Zhang and Yang Zhao Department of Mathematics Nanchang University Nanchang Jiangxi 330031 China Correspondence should be addressed to Huabin Chen chb_00721@ Received 24 March 2010 Revised 9 July 2010 Accepted 28 July 2010 Academic Editor Claudio Cuevas Copyright 2010 Huabin Chen et al. 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. By applying the Banach fixed point theorem and using an inequality technique we investigate a kind of random impulsive integrodifferential equations of neutral type. Some sufficient conditions which can guarantee the existence uniqueness and exponential stability in mean square for such systems are obtained. Compared with the previous works our method is new and our results can generalize and improve some existing ones. Finally an illustrative example is given to show the effectiveness of the proposed results. 1. Introduction Since impulsive differential systems have been highly recognized and applied in a wide spectrum of fields such as mathematical modeling of physical systems technology population and biology etc. some qualitative properties of the impulsive differential equations have been investigated by many researchers in recent years and a lot of valuable results have been obtained see . 1-10 and references therein . For the general theory of impulsive differential systems the readers can refer to 11 12 . For an impulsive differential equations if its impulsive effects are random variable their solutions are stochastic processes. It is different from the deterministic impulsive differential .
