Practical stability in terms of two measures for impulsive differential equations with ``supremum''
type: Item
instance of: scholarly article
title: Practical stability in terms of two measures for impulsive differential equations with ``supremum''
zbMATH Open document ID: 1239.34089
DOI: 10.1155/2011/703189
published in: International Journal of Differential Equations
publication date: 2012-03-08T00:00:00Z
review text: Summary: 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 for 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.
Mathematics Subject Classification ID: 34K20
Mathematics Subject Classification ID: 34K45
zbMATH DE Number: 6013215
zbMATH Keywords: Razumikhin method
zbMATH Keywords: comparison scalar equation
Wikidata QID: Q58686825
author: Snezhana Hristova
author: A. Georgieva
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2011/703189
OpenAlex ID: W2043196704
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description: scientific article; zbMATH DE number 6013215