Acta Mathematica Sinica, English Series

, Volume 30, Issue 5, pp 881–898

Square-mean almost periodic solutions to some stochastic evolution equations

Article

DOI: 10.1007/s10114-013-1109-4

Cite this article as:
Li, X.L. Acta. Math. Sin.-English Ser. (2014) 30: 881. doi:10.1007/s10114-013-1109-4

Abstract

This paper concerns the square-mean almost periodic mild solutions to a class of abstract nonautonomous functional integro-differential stochastic evolution equations in a real separable Hilbert space. By using the so-called “Acquistapace-Terreni” conditions and the Banach fixed point theorem, we establish the existence, uniqueness and the asymptotical stability of square-mean almost periodic solutions to such nonautonomous stochastic differential equations. As an application, almost periodic solution to a concrete nonautonomous stochastic integro-differential equation is considered to illustrate the applicability of our abstract results.

Keywords

Square-mean almost periodicity functional integro-differential equations “Acquistapace-Terreni” conditions evolution family 

MR(2010) Subject Classification

34C27 34D05 34F05 34G20 34K14 60H20 

Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.School of Mathematics and Information SciencesShandong Institute of Business and TechnologyYantaiP. R. China

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