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STABILITY IN THE α-NORM FOR SOME STOCHASTIC PARTIAL FUNCTIONAL INTEGRODIFFERENTIAL EQUATIONS

Diop, Mamadou Abdoul;Ezzinbi, Khalil;Lo, Modou

  • Received : 2018.02.17
  • Accepted : 2018.05.30
  • Published : 2019.01.01

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.

Keywords

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