RESPONSE SOLUTIONS OF A CLASS OF DEGENERATE QUASI-PERIODIC SYSTEMS WITH A SMALL PARAMETER

被引：1

作者：

Yang, Xiaomei ^{[1
,2
]}

Xu, Junxiang ^{[3
]}

机构：

[1] Nanjing Univ, Dept Math, Nanjing 210093, Peoples R China

[2] Jinling Inst Technol, Coll Sci, Nanjing 211169, Peoples R China

[3] Southeast Univ, Sch Math, Nanjing 210096, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2024年 / 44卷 / 02期

关键词：

Quasi-periodic systems; KAM-iteration; Diophantine condition; de-generate equilibrium point; DIFFERENTIAL-EQUATIONS; EQUILIBRIUM-POINT; INVARIANT TORI; PERTURBATIONS;

D O I：

10.3934/dcds.2023114

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers a special class of quasi-periodic systems with a small parameter, whose unperturbed part has a degenerate equilibrium point. We prove the existence of response solutions for many sufficiently small parameters. The proof is based on some formal KAM techniques and the LeraySchauder Continuation Theorem.

引用

页码：537 / 551

页数：15

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