All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
Volume 10, Number 2, 2020, Pages 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,Xiumei Jia
Keywords:Impulsive stochastic perturbed partial differential equations, Ste-panov-like pseudo almost periodic solutions, optimal controls, fractional power operators, fixed point.
      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.
PDF      Download reader