Banach空间上一类非自治微分方程的不变稳定流形  

Invariant Stable Manifolds for A Class of Non-autonomous Differential Equations on Banach Spaces

作　　者：胡洪仁 HU Hongren(School of Mathematics and Statistics,Jiangxi Normal University,330022,Nanchang,PRC)

机构地区：[1]江西师范大学数学与统计学院,南昌330022

出　　处：《江西科学》2025年第1期110-115,共6页Jiangxi Science

基　　金：国家自然科学基金项目(12361023);江西师范大学研究生创新基金项目(YJS2023073)。

摘　　要：研究了Banach空间上一类抽象非自治微分方程:u'(t)=A(t)u(t)+f(t,u(t)),t≥t_(0)不变稳定流形的存在性,其中t_(0)∈R,A(t)=a(t)A,a:R→R^(+)在R上局部可积,A是未必稠定的Hille-Yosida算子;f:R×X→X是Lipschitz函数。相比于已有的相关研究结果,上述方程的算子A(t)是未必稠定的,应用Lyapunov-Perron方法得到了上述方程不变稳定流形的存在性。In this study,the existence of invariant stable manifolds for a class of abstract nonautonomous differential equations u'(t)=A(t)u(t)+f(t,u(t)),t≥t_(0),t_(0)∈R on Banach Space X is proved,where A(t)=a(t)A,a:R→R^(+)is locally integral,A is a Hille-Yosida operator with its domain is not necessarily dense.f is a Lipschitz continuous function.Compared with the results of relevant studies,the operator of the above equation is not necessarily densely defined,and the invariant stable manifold of the above abstract non-autonomous differential equation is obtained by applying the Lyapunov-Perron method.

关 键 词：Hille-Yosida算子 未必稠定 稳定流形 抽象非自治方程 

分 类 号：O177.92[理学—数学]