Stability in the $\mathbf\alpha$-norm for some stochastic partial functional integrodifferential equations

다국어 초록 (Multilingual Abstract)

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.

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