Stability in the $\mathbf\alpha$-norm for some stochastic partial functional integrodifferential equations
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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.
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.
참고문헌 (18)
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