Quasi-periodic solutions for the two-dimensional systems with an elliptic-type degenerate equilibrium point under small perturbations

Jinjing Jiao; Guanghua Shi

doi:10.3934/cpaa.2020231

Article Contents

2020, Volume 19, Issue 11: 5157-5180. Doi: 10.3934/cpaa.2020231

This issue Previous Article Uniform stabilization of the Klein-Gordon system Next Article A non-autonomous bifurcation problem for a non-local scalar one-dimensional parabolic equation

Quasi-periodic solutions for the two-dimensional systems with an elliptic-type degenerate equilibrium point under small perturbations

Jinjing Jiao and
Guanghua Shi^,

College of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410006, China

^* Corresponding author
^* Corresponding author

Received: October 31, 2019

Revised: April 30, 2020

Early access: September 2020

Published: November 2020

The second author is supported by the Education Department Project of Hunan Province (No.18C0026) and the NNSF of China (No.11971163)

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Abstract

In this paper, we consider the existence of quasi-periodic solutions for the two-dimensional systems with an elliptic-type degenerate equilibrium point under small perturbations. We prove that under appropriate hypotheses there exist quasi-periodic solutions for perturbed ODEs near the equilibrium point for most parameter values.

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Mathematics Subject Classification: Primary: 34J40, 34C27; Secondary: 34E20.

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