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.
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页数：30
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