Exponential stability of nonlinear impulsive neutral differential equations with delays

2007 ◽  
Vol 67 (5) ◽  
pp. 1426-1439 ◽  
Author(s):  
Daoyi Xu ◽  
Zhiguo Yang ◽  
Zhichun Yang
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Neutral Differential Equations ◽  
Impulsive Neutral Differential Equations

scholarly journals The Boundedness and Exponential Stability Criterions for Nonlinear Hybrid Neutral Stochastic Functional Differential Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaofeng Zong ◽  
Fuke Wu ◽  
Chengming Huang
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Linear Growth ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Neutral Differential Equations ◽  
Linear Growth Condition ◽  
Functional Differential ◽  
Theoretical Results ◽  
Stochastic Functional

Neutral differential equations have been used to describe the systems that not only depend on the present and past states but also involve derivatives with delays. This paper considers hybrid nonlinear neutral stochastic functional differential equations (HNSFDEs) without the linear growth condition and examines the boundedness and exponential stability. Two illustrative examples are given to show the effectiveness of our theoretical results.

scholarly journals Property of oscillation of first order impulsive neutral differential equations with positive and negative coefficients

2019 ◽  
Vol 11 (1) ◽  
Author(s):  
Hussain Ali Mohamad ◽  
Aqeel Falih Jaddoa
Keyword(s):  
Differential Equation ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Variable Coefficients ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
Variable Delays ◽  
Impulsive Neutral Differential Equations ◽  
Necessary And Sufficient

            In this paper, necessary and sufficient conditions for oscillation are obtained, so that every solution of the linear impulsive neutral differential equation with variable delays and variable coefficients oscillates. Most of authors who study the oscillatory criteria of impulsive neutral differential equations, investigate the case of constant delays and variable coefficients. However the points of impulsive in this paper are more general. An illustrate example is given to demonstrate our claim and explain the results.

scholarly journals Oscillation Criteria for Solutions of Neutral Differential Equations of Impulses Effect with Positive and Negative Coefficients

2020 ◽  
Vol 17 (2) ◽  
pp. 0537
Author(s):  
Aqeel Jaddoa et al.
Keyword(s):  
Differential Equations ◽  
Sufficient Conditions ◽  
Impulsive Conditions ◽  
Neutral Differential Equations ◽  
First Order ◽  
Positive And Negative Coefficients ◽  
Oscillation Property ◽  
All Solutions ◽  
Impulsive Neutral Differential Equations ◽  
Necessary And Sufficient

In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.

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