Journal of the
Korean Mathematical Society JKMS

In this work, we study the existence, uniqueness and stability in the $\alpha$-norm of solutions for some stochastic partial functional integrodifferential equations. We suppose that the linear part has an analytic resolvent operator in the sense given in Grimmer \cite{GP} and the nonlinear part satisfies a H\"older type condition with respect to the $\alpha$-norm associated to the linear part. Firstly, we study the existence of the mild solutions. Secondly, we study the exponential stability in pth moment ($p > 2$). Our results are illustrated by an example. This work extends many previous results on stochastic partial functional differential equations.

Keywords: analytic resolvent operators, fractional power, stochastic partial functional integrodifferential equations, Wiener process, Picard iteration, mild solution, exponential stability

MSC numbers: Primary 34K30; Secondary 60H30

Supported by: The work of the authors is supported by CEA-MITIC-UGB(Senegal) and Reseau EDP-Modelisation et Controle.