Response solutions of 2-dimensional degenerate systems under quasi-periodic perturbations

被引：1

作者：

Ma, Zhichao ^{[1
,2
]}

Qu, Ru ^{[1
]}

Xu, Junxiang ^{[1
]}

机构：

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

[2] Nanjing Forestry Univ, Coll Sci, Nanjing 210037, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 360卷

基金：

中国国家自然科学基金;

关键词：

Quasi-periodic system; Degenerate equilibrium point; KAM iteration; Response solution; TORI;

D O I：

10.1016/j.jde.2023.03.046

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This paper considers quasi-periodic perturbations of 2-dimensional degenerate systems. It is proved that if the equilibrium point of the unperturbed system is hyperbolic-type degenerate, then the perturbed sys-tem has a small response solution. The proof is based on the topological degree theory and some KAM techniques developed in [3]. (c) 2023 Elsevier Inc. All rights reserved.

引用

页码：500 / 522

页数：23

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