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Perturbed Impulsive Neutral Stochastic Functional Differential Equations

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Abstract

This paper studies the asymptotic behavior of the mild solution for a class of perturbed impulsive neutral stochastic functional differential equations driven by fractional Brownian motion in Hilbert space. We establish the conditions under which the mild solutions of perturbed impulsive neutral stochastic functional differential equation and the unperturbed one are close on finite time interval when the perturbation tends to zero. Moreover, we show the result holds on time interval whose length tends to infinity as the perturbation tends to zero. As an application, the asymptotic behavior of the mild solution for a class of perturbed impulsive neutral stochastic partial differential equations driven by fractional Brownian motion in Hilbert space is proposed to show the feasibility of the obtained result.

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Acknowledgements

The authors are deeply grateful to the editor and anonymous referees for the careful reading, valuable comments and correcting some errors, which have greatly improved the quality of the paper.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang, 4524048, China

    Lijuan Cheng

  2. Department of Mathematics, Anhui Normal University, Wuhu, 241000, China

    Lanying Hu & Yong Ren

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  1. Lijuan Cheng
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  2. Lanying Hu
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  3. Yong Ren
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Correspondence to Yong Ren.

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This work is supported by the National Natural Science Foundation of China (11871076).

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Cheng, L., Hu, L. & Ren, Y. Perturbed Impulsive Neutral Stochastic Functional Differential Equations. Qual. Theory Dyn. Syst. 20, 27 (2021). https://doi.org/10.1007/s12346-021-00469-7

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