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

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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.

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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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Authors and Affiliations

  1. Department of Mathematics, Shanghai Key Laboratory of PMMP, East China Normal University, Shanghai, 200241, People’s Republic of China

    Fatima Zahra Mokkedem & Xianlong Fu

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  1. Fatima Zahra Mokkedem
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  2. Xianlong Fu
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Correspondence to Xianlong Fu.

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Mokkedem, F.Z., Fu, X. Approximate Controllability for a Semilinear Stochastic Evolution System with Infinite Delay in \(L_p\) Space. Appl Math Optim 75, 253–283 (2017). https://doi.org/10.1007/s00245-016-9332-x

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