一类中立型随机发展方程解的存在性与正则性  

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

作　　者：宋玉莹 范虹霞[1] Yuying Song;Hongxia Fan(College of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070)

机构地区：[1]兰州交通大学数理学院,兰州730070

出　　处：《数学物理学报（A辑）》2023年第1期238-248,共11页Acta Mathematica Scientia

基　　金：国家自然科学基金(11561040)。

摘　　要：该文在Hilbert空间中研究一类中立型随机偏泛函积分微分方程解的存在性与正则性.利用预解算子理论及不动点定理获得Hilbert空间X及Xα上mild解的存在性结果,且验证在某些条件下方程的mild解就是其古典解,推广已有的相关结果.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 Xa are obtained.It is verified that the mild solution of the equation is its classical solution under some conditions,which generalizes the relevant results.

关 键 词：中立型随机积分微分方程 正则性 MILD解 预解算子理论 不动点定理 

分 类 号：O175.6[理学—数学]