Quasi-periodic Response Solution to Scalar State-Dependent Delay Differential Equation with Degenerate Equilibrium

被引：0

作者：

He, Xiaolong ^{[1
]}

Jin, Feng ^{[1
]}

Song, Yongli ^{[1
]}

机构：

[1] Hangzhou Normal Univ, Dept Math, Hangzhou 311121, Peoples R China

来源：

QUALITATIVE THEORY OF DYNAMICAL SYSTEMS | 2024年 / 23卷 / 05期

基金：

中国国家自然科学基金;

关键词：

State-dependent delay; Quasi-periodic; Parameterization method; KAM; Degenerate equilibrium; PARAMETERIZATION METHOD; MANIFOLDS; PERTURBATION; CONSTRUCTION; C-1-SMOOTHNESS; ANALYTICITY; PERSISTENCE; REGULARITY; ORBITS;

D O I：

10.1007/s12346-024-01104-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider the state-dependent delay differential equation (SDDE) obtained by adding delayed perturbation to a one-dimensional ODE with a degenerate equilibrium. We prove the existence of the response solution of the equation, i.e., the quasi-periodic solution with the same frequency as the forcing. The novelty of our paper is to provide a concrete example to discuss the smoothness issues of SDDE, especially showing the analyticity of quasi-periodic solutions in some probability sense.

引用

页数：30

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