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Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method

Published online by Cambridge University Press:  17 February 2009

D. D. Bainov  and
I. M. Stamova
D. D. Bainov
Affiliation:
Medical University of Sofia, P.O. Box 45, 1504 Sofia, Bulgaria.
I. M. Stamova
Affiliation:
Technical University, Sliven, Bulgaria.
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Abstract

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We consider the stability of the zero solution of a system of impulsive functional-differential equations. By means of piecewise continuous functions, which are generalizations of classical Lyapunov functions, and using a technique due to Razumikhin, sufficient conditions are found for stability, uniform stability and asymptotical stability of the zero solution of these equations. Applications to impulsive population dynamics are also discussed.

Type
Research Article
Information
The ANZIAM Journal , Volume 43 , Issue 2 , October 2001 , pp. 269 - 278
Copyright
Copyright © Australian Mathematical Society 2001

References

[1]Bainov, D. D., Covachev, V. C. and Stamova, I. M., “Estimates of the solutions of impulsive quasilinear functional differential equations”, Ann. Fac. Sci. de Toulouse 2 (1991) 149–161.CrossRefGoogle Scholar
[2]Bainov, D. D., Covachev, V. C. and Stamova, I. M., “Stability under persistent disturbances of impulsive differential-difference equations of neutral type”, J. Math. Anal. Appl. 187 (1994) 790–808.CrossRefGoogle Scholar
[3]Bainov, D. D., Kulev, G. K. and Stamova, I. M., “Global stability of the solutions of impulsive differential-difference equations”, SUT J. of Math. 31 (1995) 55–71.CrossRefGoogle Scholar
[4]Bainov, D. D. and Simeonov, P. S., Systems with impulse effect: stability, theory and applications (Ellis Horwood, Chichester, 1989).Google Scholar
[5]Lakshmikantham, V., “Functional differential systems and extension of Lyapunov's method”, J. Math. Anal. Appl. 8 (1964) 392–405.CrossRefGoogle Scholar
[6]Lakshmikantham, V., Leela, S. and Martynyuk, A. A., Stability analysis of nonlinear systems (Marcel Dekker, New York, 1989).Google Scholar
[7]Razumikhin, B. S., Stability of systems with retardation, in Russian (Nauka, Moscow, 1988).Google Scholar