In this paper, approximate controllability for a class of infinite-delayed semilinear stochastic systems in $$L_p$$ L p space ( $$2<p<\infty $$ 2 < p < ∞ ) 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.
Applied Mathematics and Optimization – Springer Journals
Published: Feb 11, 2016
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