STEPANOV-LIKE PSEUDO ALMOST PERIODIC SOLUTIONS FOR IMPULSIVE PERTURBED PARTIAL STOCHASTIC DIFFERENTIAL EQUATIONS AND ITS OPTIMAL CONTROL

Zuomao Yan; Xiumei Jia

doi:10.11948/20180304

2020 Volume 10 Issue 2

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Zuomao Yan, Xiumei Jia. STEPANOV-LIKE PSEUDO ALMOST PERIODIC SOLUTIONS FOR IMPULSIVE PERTURBED PARTIAL STOCHASTIC DIFFERENTIAL EQUATIONS AND ITS OPTIMAL CONTROL[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 530-568. doi: 10.11948/20180304

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Zuomao Yan, Xiumei Jia. STEPANOV-LIKE PSEUDO ALMOST PERIODIC SOLUTIONS FOR IMPULSIVE PERTURBED PARTIAL STOCHASTIC DIFFERENTIAL EQUATIONS AND ITS OPTIMAL CONTROL[J]. Journal of Applied Analysis & Computation, 2020, 10(2): 530-568. doi: 10.11948/20180304

STEPANOV-LIKE PSEUDO ALMOST PERIODIC SOLUTIONS FOR IMPULSIVE PERTURBED PARTIAL STOCHASTIC DIFFERENTIAL EQUATIONS AND ITS OPTIMAL CONTROL

Zuomao Yan^1, ,,
Xiumei Jia¹

1.
Department of Mathematics, Hexi University, Zhangye, Gansu 734000, China

Corresponding author: Email address: yanzuomao@163.com(Z. Yan)
Fund Project: The authors were supported by National Natural Science Foundation of China (11461019)

Abstract

Abstract

This paper is mainly concerned with the Stepanov-like pseudo almost periodicity to a class of impulsive perturbed partial stochastic differential equations. Firstly, we prove the existence of p-mean piecewise Stepanov-like pseudo almost periodic mild solutions for the impulsive stochastic dynamical system in a Hilbert space under non-Lipschitz conditions. The results are obtained by using the fixed point techniques with fractional power arguments. Then the existence of optimal pairs of system governed by impulsive partial stochastic differential equations is also obtained. Finally, an example is provided to illustrate the developed theory.
- Impulsive stochastic perturbed partial differential equations /
- Stepanov-like pseudo almost periodic solutions /
- optimal controls /
- fractional power operators /
- fixed point
MSC: 34A37, 60H10, 35B15, 43A60, 93E20

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References

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