Razumikhin techniques in impulsive functional differential equations. (English) Zbl 0939.34071

Shen, J. H.

Nonlinear Anal., Theory Methods Appl. 36, No. 1, A, 119-130 (1999).

Here, impulsive functional-differential equations are considered. The uniform stability for such equations is proved by extending the Lyapunov- Razumikhin theorems to impulsive functional-differential equations. Some examples are given.

Reviewer: Angela Slavova (Sofia)

MSC:

34K45	Functional-differential equations with impulses
34A37	Ordinary differential equations with impulses

Keywords:

differential equations with impulses; stability theory

References:

[1]	Anokhin, A.V., On linear impulsive systems for functional differential equations, Soviet math. dokl., 33, 220-223, (1986) · Zbl 0615.34064
[2]	Anokhin, A.V.; Berezansky, L.; Braverman, E., Exponential stability of linear delay impulsive differential equations, J. math. anal. appl., 193, 923-941, (1995) · Zbl 0837.34076
[3]	Bainov, D.D.; Covachev, V.; Stamova, I., Estimates of the solutions of impulsive quasilinear functional differential equations, Ann. fac. sci. Toulouse, 12, 149-161, (1991) · Zbl 0749.34039
[4]	Bainov, D.D.; Covachev, V.; Stamova, I., Stability under persistent disturbances of impulsive differential-difference equations of neutral type, J. math. anal. appl., 187, 790-808, (1994) · Zbl 0811.34057
[5]	Bainov, D.D.; Dishliev, A.; Stamova, I., Lipschitz quasistability of impulsive differential-difference equations with variable impulsive perturbations, J. comput. appl. math., 70, 267-277, (1996) · Zbl 0854.34073
[6]	Bainov, D.D.; Kulev, G.; Stamova, I., Global stability of the solutions of impulsive differential-difference equations, SUT J. math., 31, 55-71, (1995) · Zbl 0833.34070
[7]	Bainov, D.D.; Simeonov, P.S., Stability with respect to part of the variable in systems with impulse effect, J. math. anal. appl., 117, 247-263, (1986) · Zbl 0588.34044
[8]	Bainov, D.D.; Simeonov, P.S., Systems with impulse effect: stability theory and applications, (1989), Ellis Horwood Chichester · Zbl 0676.34035
[9]	Bainov, D.D.; Stamova, I., Uniform asymptotic stability of impulsive differential-difference equations of neutral type by Lyapunov direct methods, J. comput. appl. math., 62, 359-369, (1995) · Zbl 0848.34057
[10]	Gopalsamy, K.; Zhang, B.G., On delay differential equations with impulses, J. math. anal. appl., 139, 110-122, (1989) · Zbl 0687.34065
[11]	Lakshmikantham, V.; Bainov, D.D.; Simeonov, P.S., Theory of impulsive differential equations, (1989), World Scientific Singapore · Zbl 0719.34002
[12]	Lakshmikantham, V.; Liu, X.Z., Stability analysis in terms of two measures, (1993), World Scientific Singapore · Zbl 0797.34056
[13]	Shen, J.H., Existence and uniqueness of solutions for impulsive functional differential equations on the PC space with applications, Acta sci. nat. univ. norm. hunan, 19, 13-17, (1996)