scholarly journals Necessary and sufficient conditions for nonoscillatory solutions of impulsive delay differential equations

2013 ◽  
pp. 1-18
Author(s):  
Shao Yuan Huang ◽  
Sui Sun Cheng
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Nonoscillatory Solutions ◽  
Impulsive Delay Differential Equations ◽  
Impulsive Delay ◽  
Delay Differential ◽  
Necessary And Sufficient

Oscillation of the Riemann–Weber Version of Euler Differential Equations with Delay

2000 ◽  
Vol 7 (3) ◽  
pp. 577-584
Author(s):  
Jitsuro Sugie ◽  
Mitsuru Iwasaki
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Delay Differential ◽  
Necessary And Sufficient ◽  
Equations With Delay ◽  
Oscillation Of Solutions

Abstract Our concern is to consider delay differential equations of Euler type. Necessary and sufficient conditions for the oscillation of solutions are given. The results extend some famous facts about Euler differential equations without delay.

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 The Oscillation of a Class of the Fractional-Order Delay Differential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Qianli Lu ◽  
Feng Cen
Keyword(s):  
Differential Equations ◽  
Fractional Order ◽  
Delay Differential Equations ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Analysis Method ◽  
Constant Coefficients ◽  
Delay Differential ◽  
Necessary And Sufficient

Several oscillation results are proposed including necessary and sufficient conditions for the oscillation of fractional-order delay differential equations with constant coefficients, the sufficient or necessary and sufficient conditions for the oscillation of fractional-order delay differential equations by analysis method, and the sufficient or necessary and sufficient conditions for the oscillation of delay partial differential equation with three different boundary conditions. For this,α-exponential function which is a kind of functions that play the same role of the classical exponential functions of fractional-order derivatives is used.

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 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.

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