Strict stability in terms of two measures for impulsive differential equations with ‘supremum’

2012 ◽  
Vol 91 (7) ◽  
pp. 1379-1392 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Snezhana Hristova
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Strict Stability ◽  
Two Measures

scholarly journals On the Practical Stability of Impulsive Differential Equations with Infinite Delay in Terms of Two Measures

2012 ◽  
Vol 2012 ◽  
pp. 1-8 ◽  
Author(s):  
Bo Wu ◽  
Jing Han ◽  
Xiushan Cai
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Infinite Delay ◽  
Impulsive Differential Equations ◽  
Practical Stability ◽  
Stability Criteria ◽  
Razumikhin Technique ◽  
Two Measures

We consider the practical stability of impulsive differential equations with infinite delay in terms of two measures. New stability criteria are established by employing Lyapunov functions and Razumikhin technique. Moreover, an example is given to illustrate the advantage of the obtained result.

Stability on a cone in terms of two measures for impulsive differential equations with “supremum”

2009 ◽  
Author(s):  
Snezhana G. Hristova ◽  
George Venkov ◽  
Ralitza Kovacheva ◽  
Vesela Pasheva
Keyword(s):  
Differential Equations ◽  
Impulsive Differential Equations ◽  
Two Measures

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

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
S. G. Hristova ◽  
A. Georgieva
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Practical Stability ◽  
Time Interval ◽  
Comparison Results ◽  
Two Measures ◽  
The Stability ◽  
The Given ◽  
Stability Concepts

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.

scholarly journals Integralφ0-Stability in terms of Two Measures for Impulsive Differential Equations with “Supremum”

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Peiguang Wang ◽  
Xiaojing Liu ◽  
Qing Xu
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Comparative Method ◽  
Impulsive Differential Equations ◽  
Two Measures ◽  
Piecewise Continuous

This paper establishes a criterion on integralφ0-stability in terms of two measures for impulsive differential equations with “supremum” by using the cone-valued piecewise continuous Lyapunov functions, Razumikhin method, and comparative method. Meantime, an example is given to illustrate our result.

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