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Pseudo Almost Periodic Solutions to Impulsive Non-autonomous Stochastic Differential Equations with Unbounded Delay and its Optimal Control

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Abstract

This paper is concerned with the pseudo almost periodic in distribution mild solutions for impulsive non-autonomous stochastic differential equations with unbounded delay and optimal controls in Hilbert spaces. Firstly, a suitable pseudo almost periodic in distribution mild solutions is introduced. The existence of pseudo almost periodic in distribution mild solutions are proved by means of a fixed-point theorem for condensing maps combined with stochastic analysis theory and evolution family. Secondly, the existence of optimal pairs of system governed by impulsive non-autonomous stochastic differential equations is also presented. Finally, an example is given for demonstration.

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Acknowledgments

The authors would like to thank the referee for his careful reading of the paper.

Funding

This work is supported by the National Natural Science Foundation of China (11461019), the President Fund of Scientific Research Innovation and Application of Hexi University (xz2013-10), and the Scientific Research Fund of Young Teacher of Hexi University (QN2015-01).

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Authors and Affiliations

  1. Department of Mathematics, Hexi University, Zhangye, Gansu, 734000, People’s Republic of China

    Zuomao Yan & Fangxia Lu

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  1. Zuomao Yan
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  2. Fangxia Lu
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Correspondence to Zuomao Yan.

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Yan, Z., Lu, F. Pseudo Almost Periodic Solutions to Impulsive Non-autonomous Stochastic Differential Equations with Unbounded Delay and its Optimal Control. J Dyn Control Syst 25, 45–78 (2019). https://doi.org/10.1007/s10883-018-9397-8

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  • DOI: https://doi.org/10.1007/s10883-018-9397-8

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