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.

scholarly journals EVENTUAL STABILITY AND EVENTUAL BOUNDEDNESS FOR IMPULSIVE DIFFERENTIAL EQUATIONS WITH “SUPREMUM”

2011 ◽  
Vol 16 (1) ◽  
pp. 304-314 ◽  
Author(s):  
Ivanka Stamova
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Lyapunov Functions ◽  
Impulsive Differential Equations ◽  
Comparison Method ◽  
Applied Method ◽  
Piecewise Continuous ◽  
Eventual Stability

Eventual stability and eventual boundedness for nonlinear impulsive differential equations with supremums are studied. The impulses take place at fixed moments of time. Piecewise continuous Lyapunov functions have been applied. Method of Razumikhin as well as comparison method for scalar impulsive ordinary differential equations have been employed.

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.

Uniform practical stability in terms of two measures with effect of delay at the time of impulses

2016 ◽  
Vol 0 (0) ◽  
Author(s):  
Palwinder Singh ◽  
Sanjay K. Srivastava ◽  
Kanwalpreet Kaur
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Practical Stability ◽  
Two Measures ◽  
Piecewise Continuous ◽  
Functional Differential

AbstractIn this paper, some sufficient conditions for uniform practical stability of impulsive functional differential equations in terms of two measures with effect of delay at the time of impulses are obtained by using piecewise continuous Lyapunov functions and Razumikhin techniques. The application of obtained result is illustrated with an example.

scholarly journals Stability of the solutions of impulsive functional-differential equations by Lyapunov's direct method

2001 ◽  
Vol 43 (2) ◽  
pp. 269-278 ◽  
Author(s):  
D. D. Bainov ◽  
I. M. Stamova
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Direct Method ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Continuous Functions ◽  
Piecewise Continuous ◽  
Functional Differential ◽  
The Stability

AbstractWe consider the stability of the zero solution of a system of impulsive functional-differential equations. By means of piecewise continuous functions, which are generalizations of classical Lyapunov functions, and using a technique due to Razumikhin, sufficient conditions are found for stability, uniform stability and asymptotical stability of the zero solution of these equations. Applications to impulsive population dynamics are also discussed.

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