On small perturbations of a nonlinear periodic system with degenerate equilibrium

被引：6

作者：

Lu, Xuezhu ^{[1
]}

Xu, Junxiang ^{[1
]}

机构：

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

来源：

NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2014年 / 21卷 / 03期

关键词：

Periodic system; Degenerate equilibrium; Small perturbation; Reducibility; REDUCIBILITY;

D O I：

10.1007/s00030-013-0250-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper considers the reducibility and existence of periodic solutions for a class of nonlinear periodic system with a degenerate equilibrium point under small perturbations. By introducing some parameter, we consider an equivalent periodic system. Then we prove that by an affine linear periodic transformation the parameterized periodic system is reducible to one with zero as an equilibrium. Topological degree theorem ensures that for some parameter the result can go back to the original system. Then, we obtain a small periodic solution.

引用

页码：361 / 370

页数：10

共 50 条

[1] On small perturbations of a nonlinear periodic system with degenerate equilibrium
Xuezhu Lu
Junxiang Xu
[J]. Nonlinear Differential Equations and Applications NoDEA, 2014, 21 : 361 - 370
[2] On the reducibility of a nonlinear periodic system with degenerate equilibrium
Liang, Jianli
Tang, Longkun
[J]. DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2018, 33 (02): : 239 - 252
[3] Reducibility for a Class of Almost-Periodic Differential Equations with Degenerate Equilibrium Point under Small Almost-Periodic Perturbations
Qiu, Wenhua
Si, Jianguo
[J]. ABSTRACT AND APPLIED ANALYSIS, 2013,
[4] Small parameter perturbations of nonlinear periodic systems
Kamenskii, M
Makarenkov, O
Nistri, P
[J]. NONLINEARITY, 2004, 17 (01) : 193 - 205
[5] On the Reducibility of a Class of Nonlinear Periodic Hamiltonian Systems with Degenerate Equilibrium
Jia Li
[J]. Qualitative Theory of Dynamical Systems, 2020, 19
[6] On the Reducibility of a Class of Nonlinear Periodic Hamiltonian Systems with Degenerate Equilibrium
Li, Jia
[J]. QUALITATIVE THEORY OF DYNAMICAL SYSTEMS, 2020, 19 (02)
[7] Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations
Xuemei Li
Zaijiu Shang
[J]. Journal of Dynamics and Differential Equations, 2019, 31 : 653 - 681
[8] Quasi-Periodic Solutions for Differential Equations with an Elliptic-Type Degenerate Equilibrium Point Under Small Perturbations
Li, Xuemei
Shang, Zaijiu
[J]. JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS, 2019, 31 (02) : 653 - 681
[9] ON SMALL PERTURBATION OF FOUR-DIMENSIONAL QUASI-PERIODIC SYSTEM WITH DEGENERATE EQUILIBRIUM POINT
Qiu, Wenhua
Si, Jianguo
[J]. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2015, 14 (02) : 421 - 437
[10] Response Solutions of Degenerate Quasi-Periodic Systems Under Small Perturbations
Song Ni
Junxiang Xu
[J]. Qualitative Theory of Dynamical Systems, 2023, 22

← 1 2 3 4 5 →