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] R. Grimmer. Resolvent operators for integral equations in a banach space. Transactions of the American Mathematical Society, 273(1): 333-349, 1982, 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.