On the Existence of Almost Periodic Lyapunov Functions for Impulsive Differential Equations

2000 ◽  
Vol 19 (2) ◽  
pp. 561-573 ◽  
Author(s):  
G.T. Stamov
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Impulsive Differential Equations ◽  
Almost Periodic

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.

Dynamics of an N-Species Gilpin–Ayala Impulsive Competition System

2019 ◽  
Vol 20 (7-8) ◽  
pp. 737-746
Author(s):  
Libo Wang ◽  
Guigui Xu
Keyword(s):  
Periodic Solution ◽  
Differential Equations ◽  
Lyapunov Functional ◽  
Sufficient Conditions ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solution ◽  
Asymptotical Stability ◽  
Global Asymptotical Stability ◽  
Almost Periodic ◽  
Competition System

AbstractIn this paper, we consider an N-species Gilpin–Ayala impulsive competition system. By using comparison theorem, Lyapunov functional, and almost periodic functional hull theory of the impulsive differential equations, this paper gives some new sufficient conditions for the permanence, global asymptotical stability, and almost periodic solution of the model. Our results extend some previously known results. The method used in this paper provides a possible method to study the permanence, global asymptotical stability, and almost periodic solution of the models with impulsive perturbations in biological populations.

scholarly journals Existence of Almost Periodic Solutions for a Class of Abstract Impulsive Differential Equations

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Hernán R. Henríquez ◽  
Bruno De Andrade ◽  
Marcos Rabelo
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Impulsive Differential Equations ◽  
Almost Periodic Solutions ◽  
Almost Periodic

We study the existence of piecewise almost periodic solutions for a class of abstract impulsive semilinear differential equations.

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