具有无限时滞的中立型随机泛函微分方程的分量型ψ^(γ)稳定性定理  

Razumikhin Type Theorem for Neutral Stochastic Functional Differential Equations with Infinite Delay Via Vector Lyapunov Function

作　　者：刘羽 李树勇[2] 肖可 LIU Yu;LI Shuyong;XIAO Ke(College of Mathematical Science,Sichuan Normal University,Chengdu 610066,Sichuan;School of Mathematics and Physics,Mianyang Teachers’College,Mianyang 621000,Sichuan)

机构地区：[1]四川师范大学数学科学学院,四川成都610066 [2]绵阳师范学院,四川绵阳621000

出　　处：《四川师范大学学报（自然科学版）》2022年第2期164-173,共10页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金(11571245)。

摘　　要：研究一类具有无限时滞的中立型随机泛函微分方程的稳定性问题.通过采用Razumikhin技巧和向量Lyapunov函数方法,运用It公式,建立该系统具有一般衰减稳定性的分量Razumikhin型定理,并给出系统具有一般衰减速率的p阶矩ψ^(γ)稳定和a.s.ψ^(γ)稳定的充分判据.最后,通过例子阐明结果的有效性.This paper is devoted to the investigation of the general delay stability for neutral stochastic functional differential equations with infinite delay.By using Razumikhin techniques,the vector Lyapunov function method and It formula,some vector Razumikhin-type theorems on general decay stability of the system were established.Moreover,novel sufficient criteria on theψ^(γ)stability and almost sureψ^(γ)stability of the p-th moment were obtained.Finally,one example was given to illustrate the effectiveness of the results.

关 键 词：中立型随机泛函微分方程 无限时滞 RAZUMIKHIN技巧 分量Lyapunov函数 ψ^(γ)-稳定 

分 类 号：O175.13[理学—数学] O211.63[理学—基础数学]