scholarly journals Stability Analysis of Impulsive Stochastic Functional Differential Equations with Delayed Impulses via Comparison Principle and Impulsive Delay Differential Inequality

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Pei Cheng ◽  
Fengqi Yao ◽  
Mingang Hua
Keyword(s):  
Comparison Principle ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Stochastic Functional Differential Equations ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential ◽  
Delayed Impulses ◽  
Stochastic Functional ◽  
Delay Differential Inequality

The problem of stability for nonlinear impulsive stochastic functional differential equations with delayed impulses is addressed in this paper. Based on the comparison principle and an impulsive delay differential inequality, some exponential stability and asymptotical stability criteria are derived, which show that the system will be stable if the impulses’ frequency and amplitude are suitably related to the increase or decrease of the continuous stochastic flows. The obtained results complement ones from some recent works. Two examples are discussed to illustrate the effectiveness and advantages of our results.

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 On the Oscillation of Conformable Impulsive Vector Partial Differential Equations

2020 ◽  
Vol 76 (1) ◽  
pp. 95-114
Author(s):  
George E. Chatzarakis ◽  
Kandhasamy Logaarasi ◽  
Thangaraj Raja ◽  
Vadivel Sadhasivam
Keyword(s):  
Differential Equations ◽  
Differential Inequality ◽  
Functional Differential Equations ◽  
Inner Product ◽  
One Dimensional ◽  
Inequality Technique ◽  
Impulsive Delay ◽  
Functional Differential ◽  
Delay Differential ◽  
Impulsive Differential Inequality

AbstractIn this paper, we study the oscillations of a class of conformable impulsive vector partial functional differential equations. For this class, our approach is to reduce the multi-dimensional oscillation problems to that of one dimensional impulsive delay differential inequalities by applying inner product reducing dimension method and an impulsive differential inequality technique. We provide an example to illustrate the effectiveness of our main results.

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