Journal of Dynamical and Control Systems

, Volume 25, Issue 1, pp 45–78 | Cite as

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

  • Zuomao YanEmail author
  • Fangxia Lu


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.


Impulsive non-autonomous stochastic differential equations Pseudo almost periodic in distribution functions Optimal control Unbounded delay Fixed point 

Mathematics Subject Classification (2010)

34A37 60H15 35B15 34H05 34F05 



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

Funding information

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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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsHexi UniversityZhangyePeople’s Republic of China

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