scholarly journals A New Comparison Principle for Impulsive Functional Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-6
Author(s):  
Gang Li ◽  
Weizhong Ling ◽  
Changming Ding
Keyword(s):  
Differential Equations ◽  
Comparison Principle ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Differential Systems ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential

We establish a new comparison principle for impulsive differential systems with time delay. Then, using this comparison principle, we obtain some sufficient conditions for several stabilities of impulsive delay differential equations. Finally, we present an example to show the effectiveness of our results.

scholarly journals Global Exponential Stability of Impulsive Functional Differential Equations via Razumikhin Technique

2010 ◽  
Vol 2010 ◽  
pp. 1-11 ◽  
Author(s):  
Shiguo Peng ◽  
Liping Yang
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Global Exponential Stability ◽  
Functional Differential Equations ◽  
Razumikhin Technique ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential

This paper develops some new Razumikhin-type theorems on global exponential stability of impulsive functional differential equations. Some applications are given to impulsive delay differential equations. Compared with some existing works, a distinctive feature of this paper is to address exponential stability problems for any finite delay. It is shown that the functional differential equations can be globally exponentially stabilized by impulses even if it may be unstable itself. Two examples verify the effectiveness of the proposed results.

Stability analysis of uncertain delay differential equations

2021 ◽  
pp. 1-11
Author(s):  
Jian Wang ◽  
Yuanguo Zhu
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Liu Process ◽  
Uncertain Dynamical System ◽  
Analytic Expression ◽  
Functional Differential ◽  
The One ◽  
Delay Differential

Uncertain delay differential equation is a class of functional differential equations driven by Liu process. It is an important model to describe the evolution process of uncertain dynamical system. In this paper, on the one hand, the analytic expression of a class of linear uncertain delay differential equations are investigated. On the other hand, the new sufficient conditions for uncertain delay differential equations being stable in measure and in mean are presented by using retarded-type Gronwall inequality. Several examples show that our stability conditions are superior to the existing results.

scholarly journals Oscillation of Fourth-Order Functional Differential Equations with Distributed Delay

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 61 ◽  
Author(s):  
Clemente Cesarano ◽  
Omar Bazighifan
Keyword(s):  
Differential Equations ◽  
Fourth Order ◽  
Delay Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Distributed Delay ◽  
All Solutions ◽  
Functional Differential ◽  
Delay Differential ◽  
Comparison Technique

In this paper, the authors obtain some new sufficient conditions for the oscillation of all solutions of the fourth order delay differential equations. Some new oscillatory criteria are obtained by using the generalized Riccati transformations and comparison technique with first order delay differential equation. Our results extend and improve many well-known results for oscillation of solutions to a class of fourth-order delay differential equations. The effectiveness of the obtained criteria is illustrated via examples.

scholarly journals Exponential Stability of Impulsive Delay Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
G. L. Zhang ◽  
M. H. Song ◽  
M. Z. Liu
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Euler Method ◽  
Exponentially Stable ◽  
Impulsive Delay Differential Equations ◽  
Numerical Process ◽  
Impulsive Delay ◽  
Delay Differential

The main objective of this paper is to further investigate the exponential stability of a class of impulsive delay differential equations. Several new criteria for the exponential stability are analytically established based on Razumikhin techniques. Some sufficient conditions, under which a class of linear impulsive delay differential equations are exponentially stable, are also given. An Euler method is applied to this kind of equations and it is shown that the exponential stability is preserved by the numerical process.

scholarly journals Boundary value problem for the second order impulsive delay differential equations

2015 ◽  
Vol 14 (1) ◽  
pp. 27-35
Author(s):  
Lidia Skóra
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Second Order ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential

Abstract We present some existence and uniqueness result for a boundary value problem for functional differential equations of second order with impulses at fixed points.

Exponential Stability of Impulsive Delay Differential Equations by using Weight Function

2018 ◽  
Vol 7 (3) ◽  
pp. 247-251
Author(s):  
Palwinder Singh ◽  
Sanjay K. Srivastava ◽  
Kanwalpreet Kaur
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Weight Function ◽  
Delay Differential Equations ◽  
Lyapunov Functions ◽  
Sufficient Conditions ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential

Abstract In present study, some sufficient conditions for the exponential stability of impulsive delay differential equations are obtained by introducing weight function in the norm and applying the concept of Lyapunov functions and Razumikhin techniques. The function ψ plays the role of weight and hence increases the rate of convergence towards stability. The obtained results are demonstrated with examples.

scholarly journals New Results for Oscillation of Solutions of Odd-Order Neutral Differential Equations

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1095
Author(s):  
Clemente Cesarano ◽  
Osama Moaaz ◽  
Belgees Qaraad ◽  
Nawal A. Alshehri ◽  
Sayed K. Elagan ◽  
...  
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Oscillatory Behavior ◽  
Neutral Delay ◽  
Neutral Differential Equations ◽  
Odd Order ◽  
Future Prediction ◽  
Functional Differential ◽  
Delay Differential

Differential equations with delay arguments are one of the branches of functional differential equations which take into account the system’s past, allowing for more accurate and efficient future prediction. The symmetry of the equations in terms of positive and negative solutions plays a fundamental and important role in the study of oscillation. In this paper, we study the oscillatory behavior of a class of odd-order neutral delay differential equations. We establish new sufficient conditions for all solutions of such equations to be oscillatory. The obtained results improve, simplify and complement many existing results.

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