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.
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页码：537 / 551
页数：15
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