NEW RAZUMIKHIN TYPE STABILITY THEOREM FOR IMPULSIVE FUNCTIONAL DIFFERENTIAL EQUATIONS WITH INFINITE DELAYS

2011 ◽  
Vol 09 (03) ◽  
pp. 315-327 ◽  
Author(s):  
JIAYU WANG ◽  
XIAODI LI
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Stability Theorem ◽  
Uniform Asymptotic Stability ◽  
Razumikhin Technique ◽  
Infinite Delays ◽  
Functional Differential ◽  
The Stability

In this paper, the stability of impulsive functional differential equations with infinite delays are investigated. By using Lyapunov functions and the Razumikhin technique, a new theorem on the uniform asymptotic stability and global asymptotic stability for such differential equations is obtained. An example is given to illustrate the feasibility of the result.

scholarly journals New Results on Impulsive Functional Differential Equations with Infinite Delays

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jie Yang ◽  
Bing Xie
Keyword(s):  
Differential Equations ◽  
Lyapunov Functions ◽  
Functional Differential Equations ◽  
Stability Behavior ◽  
Razumikhin Technique ◽  
Infinite Delays ◽  
Functional Differential ◽  
The Stability

We investigate the stability for a class of impulsive functional differential equations with infinite delays by using Lyapunov functions and Razumikhin-technique. Some new Razumikhin-type theorems on stability are obtained, which shows that impulses do contribute to the system’s stability behavior. An example is also given to illustrate the importance of our results.

scholarly journals On Stability of Linear Delay Differential Equations under Perron's Condition

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
J. Diblík ◽  
A. Zafer
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Zero Solution ◽  
Uniform Asymptotic Stability ◽  
Linear Delay ◽  
Functional Differential ◽  
The Stability ◽  
Delay Differential

The stability of the zero solution of a system of first-order linear functional differential equations with nonconstant delay is considered. Sufficient conditions for stability, uniform stability, asymptotic stability, and uniform asymptotic stability are established.

scholarly journals Stability and boundedness to certain differential equations of fourth order with multiple delays

Filomat ◽  
2014 ◽  
Vol 28 (5) ◽  
pp. 1049-1058 ◽  
Author(s):  
Erdal Korkmaz ◽  
Cemil Tunc
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Fourth Order ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Functional Approach ◽  
Multiple Delays ◽  
Boundedness Of Solutions ◽  
Functional Differential ◽  
The Stability

In this paper, we give sufficient conditions to guarantee the asymptotic stability and boundedness of solutions to a kind of fourth-order functional differential equations with multiple delays. By using the Lyapunov-Krasovskii functional approach, we establish two new results on the stability and boundedness of solutions, which include and improve some related results in the literature.

Sign in / Sign up

Export Citation Format

Share Document