EXISTENCE AND EXPONENTIAL STABILITY OF MILD SOLUTIONS FOR SECOND-ORDER NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION WITH RANDOM IMPULSES

Linxin Shu; Xiao-Bao Shu; Quanxin Zhu; Fei Xu

doi:10.11948/20190089

2021 Volume 11 Issue 1

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Linxin Shu, Xiao-Bao Shu, Quanxin Zhu, Fei Xu. EXISTENCE AND EXPONENTIAL STABILITY OF MILD SOLUTIONS FOR SECOND-ORDER NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION WITH RANDOM IMPULSES[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 59-80. doi: 10.11948/20190089

Citation:

Linxin Shu, Xiao-Bao Shu, Quanxin Zhu, Fei Xu. EXISTENCE AND EXPONENTIAL STABILITY OF MILD SOLUTIONS FOR SECOND-ORDER NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION WITH RANDOM IMPULSES[J]. Journal of Applied Analysis & Computation, 2021, 11(1): 59-80. doi: 10.11948/20190089

EXISTENCE AND EXPONENTIAL STABILITY OF MILD SOLUTIONS FOR SECOND-ORDER NEUTRAL STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATION WITH RANDOM IMPULSES

1.
College of Mathematics, Hunan University, Changsha, Hunan 410082, China
2.
Key Laboratory of HPC-SIP (MOE), College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China
3.
Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, N2L 3C5, Canada

Corresponding author: Email address:sxb0221@163.com(X. Shu)
Fund Project: The authors were supported by the National Natural Science Foundation of China (61773217, 61374080) and the Innovation Platforms Open Foundationof Hunan Educational Committee (541109100002)

Abstract

Abstract

In this paper, we consider the existence and exponential stability in mean square of mild solutions to second-order neutral stochastic functional differential equations with random impulses in Hilbert space. Firstly, the existence of mild solutions to the equations is proved by using the noncompact measurement strategy and the Mönch fixed point theorem. Then, the mean square exponential stability for the mild solution of the considered equations is obtained by establishing an integral inequality. Finally, an example is given to illustrate our results.
- Existence of mild solution /
- exponential stability /
- second-order neutral stochastic functional differential equation /
- random impulsive /
- It^o integrals /
- measurement of noncompact
MSC: 34K50, 34K45, 34F05

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References

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