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Lakshmikantham, V.; Liu, Xinzhi

On quasi stability for impulse differential systems. (English) Zbl 0688.34032

Nonlinear Anal., Theory Methods Appl. 13, No. 7, 819-828 (1989).
The stability notions of a given solution of an impulsive differential system cannot be transferred to the stability notions of the trivial solution by change of variables because of the fact that moments of impulsive effect of the given solution need not be the same as those of a neighbouring solution. Consequently, demanding that the difference of the given solution and a neighbouring one be small for all moments of time seems unnatural. The paper gives various notions of stability relative to a given solution and establishes some criteria for these properties.
Reviewer: L.Hatvani

Cited in 33 Documents

MSC:

34D20 Stability of solutions to ordinary differential equations
91B60 Trade models

Keywords:

comparison method; impulsive differential system
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\textit{V. Lakshmikantham} and \textit{X. Liu}, Nonlinear Anal., Theory Methods Appl. 13, No. 7, 819--828 (1989; Zbl 0688.34032)
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References:

[1] Bainov, D.D.; Simeonov, P.S., The second method of Liapunov for systems with an impulse effect, Tamk. J. math., 16, 19-40, (1985) · Zbl 0641.34051
[2] Bainov, D.D.; Simeonov, P.S., Stability with respect to part of the variables in systems with impulse effect, J. math. analysis applic, 117, 247-263, (1986) · Zbl 0588.34044
[3] Perestyuk, N.A.; Samoilenko, A.M., Differential equations with impulsive effect, (1987), Central publishers Kiev · Zbl 0837.34003
[4] {\scLakshmikantham} V. & {\scXinzhi Liu}., Stability for impulsive differential systems in terms of two measures, Appl. Math. Comp. (to appear).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.