Acta mathematica scientia,Series A ›› 2023, Vol. 43 ›› Issue (1): 238-248.

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Existence and Regularity of Solutions for a Class of Neutral Stochastic Evolution Equations

Yuying Song(),Hongxia Fan*()   

  1. College of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070
  • Received:2022-01-18 Revised:2022-07-19 Online:2023-02-26 Published:2023-03-07
  • Supported by:
    The NSFC(11561040)


In this paper, we study the existence and regularity of solutions for a class of neutral stochastic partial functional integro-differential equations in Hilbert space. By using resolvent operator theory and fixed point theorem, the existence results of mild solutions on Hilbert space $X$ and $X_{\alpha}$ are obtained. It is verified that the mild solution of the equation is its classical solution under some conditions, which generalizes the relevant results.

Key words: Neutral stochastic integro-differential equation, Regularity, Mild solution, Resolvent operator theory, Fixed point theorem

CLC Number: 

  • O175.6