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New Razumikhin type theorems for impulsive functional differential equations. (English) Zbl 1030.34078

Summary: Here, we investigate stability and boundedness for a class of impulsive functional-differential equations by using Lyapunov functions and Razumikhin technique. Some new Razumikhin-type theorems on stability and boundedness are obtained.

MSC:

34K45 Functional-differential equations with impulses
34K20 Stability theory of functional-differential equations
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References:

[1] Lakshmikantham, V.; Bainov, D.D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific Singapore · Zbl 0719.34002
[2] Bainov, D.D.; Simenov, P.S., Systems with impulse effect: stability theory and applications, (1989), Chichester Ellis Horwood
[3] Gopalsamy, K.; Zhang, B.G., On delay differential equations with impulses, J. math. anal. appl., 139, 110-122, (1989) · Zbl 0687.34065
[4] Anokhin, A.V.; Berezansky, L.; Braverman, E., Stability of linear delay impulsive differential equations, Dynamic systems appl., 4, 173-188, (1995) · Zbl 0829.34065
[5] Yu, J.S.; Zhang, B.G., Stability theorems for delay differential equations with impulses, J. math. anal. appl., 198, 285-297, (1996) · Zbl 0853.34068
[6] Shen, J.; Yan, J., Razumikhin type stability theorems for impulsive functional differential equations, Nonlinear anal., 33, 519-531, (1998) · Zbl 0933.34083
[7] X. Liu, J. Shen, Razumikhin type theorems on boundedness for impulsive functional differential equations, Dyn. Syst. Appl., accepted · Zbl 0971.34059
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