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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.
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참고문헌 (18)
참고문헌 신청
G. Da Prato / 1992 / Stochastic equations in infinite dimensions / Cambridge University Press
M. A. Diop / 2012 / Existence and uniqueness of mild solutions to some neutral stochastic partial functional integrodifferential equations with non-Lipschitz co-efficients / Int. J. Math. Math. Sci 2012:12
K. Ezzinbi / 2010 / Existence and regularity of solutions for neu-tral partial functional integrodifferential equations with infinite delay / Nonlinear Anal. Hybrid Syst 4(1):54~64
K. Ezzinbi / 2010 / Existence of solutions in the ff-norm for partial differential equations of neutral type with finite delay / Electron. J. Differential Equations (157):11
K. Ezzinbi / 2009 / Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces / Nonlinear Anal 70(9):3378~3389
M. A. Diop / 2012 / Existence and uniqueness of mild solutions to some neutral stochastic partial functional integrodifferential equations with non-Lipschitz co-efficients / Int. J. Math. Math. Sci 2012:12
K. Ezzinbi / 2010 / Existence and regularity of solutions for neu-tral partial functional integrodifferential equations with infinite delay / Nonlinear Anal. Hybrid Syst 4(1):54~64
K. Ezzinbi / 2010 / Existence of solutions in the ff-norm for partial differential equations of neutral type with finite delay / Electron. J. Differential Equations (157):11
K. Ezzinbi / 2009 / Local existence and regularity of solutions for some partial functional integrodifferential equations with infinite delay in Banach spaces / Nonlinear Anal 70(9):3378~3389
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