Báo cáo hóa học: " Research Article Integrodifferential Inequality for Stability of Singularly Perturbed Impulsive Delay "

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 Integrodifferential Inequality for Stability of Singularly Perturbed Impulsive Delay | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 369185 11 pages doi 2009 369185 Research Article Integrodifferential Inequality for Stability of Singularly Perturbed Impulsive Delay Integrodifferential Equations Danhua He1 and Liguang Xu2 1 Yangtze Center of Mathematics Sichuan University Chengdu 610064 China 2 Department of Applied Mathematics Zhejiang University of Technology Hangzhou 310023 China Correspondence should be addressed to Liguang Xu xlg132@ Received 24 February 2009 Accepted 11 June 2009 Recommended by Ondrej Dosly The exponential stability of singularly perturbed impulsive delay integrodifferential equations SPIDIDEs is concerned. By establishing an impulsive delay integrodifferential inequality IDIDI some sufficient conditions ensuring the exponentially stable of any solution of SPIDIDEs for sufficiently small e 0 are obtained. A numerical example shows the effectiveness of our theoretical results. Copyright 2009 D. He and L. Xu. 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 Integrodifferential equations IDEs arise from many areas of science from physics biology medicine etc. which have extensive scientific backgrounds and realistic mathematical models and hence have been emerging as an important area of investigation in recent years see 1-6 . Correspondingly the stability of impulsive delay integrodifferential equations has been studied quite well for example 7-9 . However besides delay and impulsive effects singular perturbation likewise exists in a wide models for physiological processes or diseases 10 . And many good results on the stability of singularly perturbed delay differential equations have been reported see for example 11-14 . Therefore it is necessary to consider delay impulse and singular .

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