International Journal of Differential Equations

Practical Stability in terms of Two Measures for Impulsive Differential Equations with “Supremum”

S. G. Hristova and A. Georgieva

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Abstract

The object of investigations is a system of impulsive differential equations with “supremum.” These equations are not widely studied yet, and at the same time they are adequate mathematical model of many real world processes in which the present state depends significantly on its maximal value on a past time interval. Practical stability for a nonlinear system of impulsive differential equations with “supremum” is defined and studied. It is applied Razumikhin method with piecewise continuous scalar Lyapunov functions and comparison results for scalar impulsive differential equations. To unify a variety of stability concepts and to offer a general framework for the investigation of the stability theory, the notion of stability in terms of two measures has been applied to both the given system and the comparison scalar equation. An example illustrates the usefulness of the obtained sufficient conditions.

Article information

Source
Int. J. Differ. Equ., Volume 2011 (2011), Article ID 703189, 13 pages.

Dates
Received: 19 May 2011
Accepted: 6 August 2011
First available in Project Euclid: 25 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1485313243

Digital Object Identifier
doi:10.1155/2011/703189

Mathematical Reviews number (MathSciNet)
MR2843511

Zentralblatt MATH identifier
1239.34089

Citation

Hristova, S. G.; Georgieva, A. Practical Stability in terms of Two Measures for Impulsive Differential Equations with “Supremum”. Int. J. Differ. Equ. 2011 (2011), Article ID 703189, 13 pages. doi:10.1155/2011/703189. https://projecteuclid.org/euclid.ijde/1485313243


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