The stability of the equilibrium of the damped oscillator with damping changing sign

被引：5

作者：

Liu, Qihuai ^{[1
]}

Qian, Dingbian ^{[1
]}

Wang, Zhiguo ^{[1
]}

机构：

[1] Suzhou Univ, Sch Math Sci, Suzhou 215006, Peoples R China

来源：

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS | 2010年 / 73卷 / 07期

基金：

国家教育部博士点专项基金资助; 中国国家自然科学基金;

关键词：

Stability; Damped oscillator; Canonical transformation; Moser's twist theorem; ASYMPTOTIC STABILITY; REVERSIBLE-SYSTEMS; DUFFING EQUATIONS; FIXED-POINTS;

D O I：

10.1016/j.na.2010.05.035

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove a sufficient and necessary condition for the stability of the equilibrium x = x' = 0 of the damped oscillator with damping changing sign x '' + h(t)x' + a(t)x(2n broken vertical bar 1) + e(t, x) = 0, n >= 1 where a(t), h(t) are continuous and 1-periodic with (h) over bar = f(0)(1) h(t)dt = 0, e(t, x) is continuous, 1-periodic in t and dominated by the power x(2n+2) in a neighborhood of x = 0. Crown Copyright (C) 2010 Published by Elsevier Ltd. All rights reserved.

引用

页码：2071 / 2077

页数：7

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