Applied Mathematics & Optimization

, Volume 75, Issue 2, pp 253–283 | Cite as

Approximate Controllability for a Semilinear Stochastic Evolution System with Infinite Delay in \(L_p\) Space

Article

Abstract

In this paper, approximate controllability for a class of infinite-delayed semilinear stochastic systems in \(L_p\) space (\(2<p<\infty \)) is studied. The fundamental solution’s theory is used to describe the mild solution which is obtained by using the Banach fixed point theorem. In this way the approximate controllability result is then obtained by assuming that the corresponding deterministic linear system is approximately controllable via the so-called the resolvent condition. An application to a Volterra stochastic equation is also provided to illustrate the obtained results.

Keywords

Stochastic evolution system Approximate controllability Fundamental solution Resolvent condition  Infinite delay 

Mathematics Subject Classification

34K30 34K35 35R10 60G99 93C10 

Notes

Acknowledgments

This work is supported by NSF of China (Nos. 11171110 and 11371087), Science and Technology Commission of Shanghai Municipality (STCSM, grant No. 13dz2260400) and Shanghai Leading Academic Discipline Project (No. B407).

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Department of Mathematics, Shanghai Key Laboratory of PMMPEast China Normal UniversityShanghaiPeople’s Republic of China

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