Existence and Stability Results of Impulsive Stochastic Partial Neutral Functional Differential Equations with Infinite Delays and Poisson Jumps

2020 ◽  
Vol 9 (2) ◽  
pp. 245-255 ◽  
Author(s):  
A. Anguraj ◽  
K. Ravikumar
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Poisson Jumps ◽  
Neutral Functional Differential Equations ◽  
Infinite Delays ◽  
Existence And Stability ◽  
Functional Differential ◽  
Stability Results

scholarly journals Existence and Exponential Stability of Solutions to Stochastic Neutral Functional Differential Equations

2017 ◽  
Vol 2017 ◽  
pp. 1-7
Author(s):  
Ling Hu ◽  
Zheng Wu ◽  
Zhangzhi Wei ◽  
Lianglong Wang
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Exponential Stability ◽  
Functional Differential Equations ◽  
Banach Fixed Point Theorem ◽  
Stability Of Solutions ◽  
Neutral Functional Differential Equations ◽  
Semigroup Approach ◽  
Existence And Stability ◽  
Functional Differential

In this paper we consider the existence and stability of solutions to stochastic neutral functional differential equations with finite delays. Under suitable conditions, the existence and exponential stability of solutions were obtained by using the semigroup approach and Banach fixed point theorem.

scholarly journals Existence and Stability Results for Second-Order Neutral Stochastic Differential Equations With Random Impulses and Poisson Jumps

2021 ◽  
Vol 1 (1) ◽  
pp. 1-18
Author(s):  
K. Ravikumar ◽  
K. Ramkumar ◽  
Dimplekumar Chalishajar
Keyword(s):  
Differential Equations ◽  
Initial Conditions ◽  
Mild Solutions ◽  
Functional Differential Equations ◽  
Banach Contraction ◽  
Existence And Stability ◽  
Random Impulses ◽  
Functional Differential ◽  
The Stability ◽  
Stability Results

The objective of this paper is to investigate the existence and stability results of secondorder neutral stochastic functional differential equations (NSFDEs) in Hilbert space. Initially, we establish the existence results of mild solutions of the aforementioned system using the Banach contraction principle. The results are formulated using stochastic analysis techniques. In the later part, we investigate the stability results through the continuous dependence of solutions on initial conditions.

Exponential stability for stochastic neutral functional differential equations driven by Rosenblatt process with delay and Poisson jumps

2016 ◽  
Vol 24 (2) ◽  
Author(s):  
El Hassan Lakhel
Keyword(s):  
Differential Equations ◽  
Functional Differential Equations ◽  
Uniqueness Result ◽  
Stochastic Functional Differential Equations ◽  
Poisson Jumps ◽  
Neutral Functional Differential Equations ◽  
Rosenblatt Process ◽  
Fixed Point Principle ◽  
Functional Differential ◽  
Stochastic Functional

AbstractIn this note we consider a class of neutral stochastic functional differential equations with finite delays driven simultaneously by a Rosenblatt process and Poisson process in a Hilbert space. We prove an existence and uniqueness result and we establish some conditions ensuring the exponential decay to zero in mean square for the mild solution by means of the Banach fixed point principle. Finally, an illustrative example is given to demonstrate the effectiveness of the obtained result.

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