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2011 Practical Stability in terms of Two Measures for Impulsive Differential Equations with “Supremum”
S. G. Hristova, A. Georgieva
Int. J. Differ. Equ. 2011: 1-13 (2011). DOI: 10.1155/2011/703189

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.

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S. G. Hristova. A. Georgieva. "Practical Stability in terms of Two Measures for Impulsive Differential Equations with “Supremum”." Int. J. Differ. Equ. 2011 1 - 13, 2011. https://doi.org/10.1155/2011/703189

Information

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

zbMATH: 1239.34089
MathSciNet: MR2843511
Digital Object Identifier: 10.1155/2011/703189

Rights: Copyright © 2011 Hindawi

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