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Global attractivity of a class of delay differential equations with impulses

Published online by Cambridge University Press:  17 February 2009

Yuji Liu
Affiliation:
Department of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China. Department of Mathematics, Yueyang Teacher's University, Yueyang, Hunan 414000, P. R. China.
Binggen Zhang
Affiliation:
Department of Mathematics, Ocean University of China, Qingdao 266071, P. R. China; e-mail: [email protected].
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Abstract

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In this paper, we study the global attractivity of the zero solution of a particular impulsive delay differential equation. Some sufficient conditions that guarantee every solution of the equation converges to zero are obtained.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Kuang, Y., Delay differential equations with applications in population dynamics (Academic Press, Boston, 1993).Google Scholar
[2]Lakshmikantham, V., Bainov, D. D. and Simenov, P. S., Theory of impulsive differential equations (World Scientific, Singapore, 1989).CrossRefGoogle Scholar
[3]Shen, J. H., “Global existence and uniqueness, oscillation and nonoscillation of impulsive delay differential equations”, Acta Math. Sinica 40 (1997) 5359, (in Chinese).Google Scholar
[4]So Joseph, W. H. and Yu, J. S., “Global attractivity for a population model with time delay”, Proc. Amer. Math. Soc. 123 (1995) 26872694.Google Scholar
[5]Wazewska-Czyzewska, M. and Lasota, A., “Mathematical problems of the dynamics of the red blood cells system”, Ann. Polon. Math. 6 (1976) 2340.Google Scholar
[6]Yu, J. S., “Global attractivity of zero solution of a class of delay differential equations and its applications”, Sci. China Ser. A 39 (1996) 225237.Google Scholar
[7]Yu, J. S., “Asymptotic stability of nonautonomous delay differential equations”, Chinese Sci. Bull. 42 (1997) 12481252.CrossRefGoogle Scholar
[8]Yu, J. S. and Zhang, B. G., “Stability theorems for delay differential equations with impulses”, J. Math. Anal. Appl. 199 (1996) 162175.CrossRefGoogle Scholar
[9]Zhang, X. S. and Yan, J. Y., “Global attractivity in impulsive functional differential equations”, Indian J. Pure Appl. Math. 29 (1998) 871878.Google Scholar