Twist periodic solutions of second order singular differential equations

被引：16

作者：

Chu, Jifeng ^{[1
]}

Li, Ming ^{[2
]}

机构：

[1] Hohai Univ, Dept Math, Coll Sci, Nanjing 210098, Peoples R China

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2009年 / 355卷 / 02期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Twist periodic solutions; Singular equations; Third-order approximation; STABILITY; EXISTENCE; EQUILIBRIUM;

D O I：

10.1016/j.jmaa.2009.02.033

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the twist periodic solutions of second order singular differential equations. Such twist periodic solutions are stable in the sense of Lyapunov and present much interesting dynamical features around them. The proof is based on the third-order approximation method. The estimates of periodic solutions of Ermakov-Pinney equations and the estimates on rotation numbers of Hill equations play an important role in the analysis. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：830 / 838

页数：9

共 19 条

[1] Periodic solutions of forced isochronous oscillators at resonance [J].

Bonheure, D ;

Fabry, C ;

Smets, D .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2002, 8 (04) :907-930

[2]

Chu JF, 2008, DISCRETE CONT DYN-A, V21, P1071

[3] INFINITELY MANY T-PERIODIC SOLUTIONS FOR A PROBLEM ARISING IN NONLINEAR ELASTICITY [J].

DELPINO, MA ;

MANASEVICH, RF .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1993, 103 (02) :260-277

[4] SUBHARMONIC SOLUTIONS FOR SOME 2ND-ORDER DIFFERENTIAL-EQUATIONS WITH SINGULARITIES [J].

FONDA, A ;

MANASEVICH, R ;

ZANOLIN, F .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1993, 24 (05) :1294-1311

[5] Multiplicity of positive periodic solutions to superlinear repulsive singular equations [J].

Jiang, DQ ;

Chu, JF ;

Zhang, M .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2005, 211 (02) :282-302

[6] ON PERIODIC-SOLUTIONS OF NONLINEAR DIFFERENTIAL-EQUATIONS WITH SINGULARITIES [J].

LAZER, AC ;

SOLIMINI, S .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 99 (01) :109-114

[7] Twist character of the least amplitude periodic solution of the forced pendulum [J].

Lei, JZ ;

Li, X ;

Yan, P ;

Zhang, MR .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2003, 35 (04) :844-867

[8] The stability of the equilibrium of a conservative system [J].

Liu, B .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1996, 202 (01) :133-149

[9]

Ortega R, 2005, TEN MATHEMATICAL ESSAYS ON APPROXIMATION IN ANALYSIS AND TOPOLOGY, P215, DOI 10.1016/B978-044451861-3/50008-2

[10] THE STABILITY OF THE EQUILIBRIUM OF A NONLINEAR HILL EQUATION [J].

ORTEGA, R .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1994, 25 (05) :1393-1401

← 1 2 →