Volume 10, Number 2, 2020, Pages 530568 DOI：10.11948/20180304 
Stepanovlike pseudo almost periodic solutions for impulsive perturbed partial stochastic differential equations and its optimal control 
Zuomao Yan,Xiumei Jia 
Keywords:Impulsive stochastic perturbed partial differential equations, Stepanovlike pseudo almost periodic solutions, optimal controls, fractional power operators, fixed point. 
Abstract: 
This paper is mainly concerned with the Stepanovlike pseudo almost periodicity to a class of impulsive perturbed partial stochastic differential equations. Firstly, we prove the existence of $p$mean piecewise Stepanovlike pseudo almost periodic mild solutions for the impulsive stochastic dynamical system in a Hilbert space under nonLipschitz 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. 
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