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 Integral Inequality and Exponential Stability for Neutral Stochastic Partial Differential Equations with Delay | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 297478 15 pages doi 2009 297478 Research Article Integral Inequality and Exponential Stability for Neutral Stochastic Partial Differential Equations with Delays Huabin Chen Department of Mathematics School of Science Nanchang University Nanchang 330031 China Correspondence should be addressed to Huabin Chen chb_00721@ Received 20 September 2009 Accepted 21 November 2009 Recommended by Jozef Banas The aim of this paper is devoted to obtain some sufficient conditions for the exponential stability in p p 2 -moment as well as almost surely exponential stability for mild solution of neutral stochastic partial differential equations with delays by establishing an integral-inequality. Some well-known results are generalized and improved. Finally an example is given to show the effectiveness of our results. Copyright 2009 Huabin Chen. 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. 1. Introduction The investigation for stochastic partial differential equations with delays has attracted the considerable attention of researchers and many qualitative theories for the solutions of this kind have been derived. Many important results have been reported in 1-20 . For example Caraballo in 1 extended the results from Haussmann 7 to the delay equations of the same kind Mao in 15 21 proved the exponential stability in mean-square sense about the strong solutions of linear stochastic differential equations with finite constant delay by using the method in 7 8 Caraballo and Real in 4 considered the stability for the strong solutions of semilinear stochastic delay evolution equations Govindan in 5 6 has studied the existence and stability of mild solutions for stochastic partial differential equations by the comparison
