Existence and asymptotic behavior of solutions for neutral stochastic partial integrodifferential equations with infinite delays

Abstract

In this work we study the existence, uniqueness and asymptotic behavior of mild solutions for neutral stochastic partial integrodifferential equations with infinite delays. To prove the results, we use the theory of resolvent operators as developed by R. Grimmer [12], as well as a version of the fixed point principle. We establish sufficient conditions ensuring that the mild solutions are exponentially stable in pth-moment. An example is provided to illustrate the abstract results.

Optimal Controls for Stochastic Functional Integrodifferential Equations M. A. Diop, P. D. A. Guindo, M. Fall, and A. Diakhaby

“…There is much current interest in studying qualitative properties for SPDEs (see, e.g., [1,2,5,26,27]). In recent years, much attention has been paid to the qualitative properties of mild solutions to various stochastic integrodifferential equations by using the resolvent operator theory for integral equations and the fixed point technique see e.g., [14,20,28] and the references therein.…”