Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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STABILITY IN THE α-NORM FOR SOME STOCHASTIC PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

  • Diop, Mamadou Abdoul (Universite Gaston Berger de Saint-Louis U.F.R. S.A.T. Departement de Mathematiques) ;
  • Ezzinbi, Khalil (Universite Cadi Ayyad Faculte des Sciences Semlalia Departement de Mathematiques) ;
  • Lo, Modou (Universite Gaston Berger de Saint-Louis U.F.R. S.A.T. Departement de Mathematiques)
  • Received : 2018.02.17
  • Accepted : 2018.05.30
  • Published : 2019.01.01
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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 [8] and the nonlinear part satisfies a $H{\ddot{o}}lder$ 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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References

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