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# International Journal of Nonlinear Sciences and Numerical Simulation

Editor-in-Chief: Birnir, Björn

Editorial Board: Armbruster, Dieter / Chen, Xi / Bessaih, Hakima / Chou, Tom / Grauer, Rainer / Marzocchella, Antonio / Rangarajan, Govindan / Trivisa, Konstantina / Weikard, Rudi

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Volume 19, Issue 5

# Pseudo Almost Periodicity and Its Applications to Impulsive Nonautonomous Partial Functional Stochastic Evolution Equations

Zuomao Yan
/ Xiumei Jia
Published Online: 2018-06-08 | DOI: https://doi.org/10.1515/ijnsns-2017-0086

## Abstract

In this paper, we establish a new composition theorem for pseudo almost periodic functions under non-Lipschitz conditions. We apply this new composition theorem together with a fixed-point theorem for condensing maps to investigate the existence of $p$-mean piecewise pseudo almost periodic mild solutions for a class of impulsive nonautonomous partial functional stochastic evolution equations in Hilbert spaces, and then, the exponential stability of $p$-mean piecewise pseudo almost periodic mild solutions is studied. Finally, an example is given to illustrate our results.

MSC 2010: 34A37; 60H10; 35B15; 34F05

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Accepted: 2018-05-20

Published Online: 2018-06-08

Published in Print: 2018-07-26

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).

Citation Information: International Journal of Nonlinear Sciences and Numerical Simulation, Volume 19, Issue 5, Pages 511–529, ISSN (Online) 2191-0294, ISSN (Print) 1565-1339,

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