Rate of decay of stable periodic solutions of Duffing equations

被引：26

作者：

Chen, Hongbin

Li, Yi ^{[1
]}

机构：

[1] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[2] Xian Jiaotong Univ, Dept Math, Xian 02982667909, Peoples R China

[3] Hunan Normal Univ, Dept Math, Changsha, Hunan, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2007年 / 236卷 / 02期

关键词：

periodic solution; stability; rate of decay;

D O I：

10.1016/j.jde.2007.01.023

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider the second-order equations of Duffing type. Bounds for the derivative of the restoring force are given that ensure the existence and uniqueness of a periodic solution. Furthermore, the stability of the unique periodic solution is analyzed; the sharp rate of exponential decay is determined for a solution that is near to the unique periodic solution. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：493 / 503

页数：11

共 50 条

[31] Exact Multiplicity and Stability of Periodic Solutions for a Duffing Equation
S. Liang
Mediterranean Journal of Mathematics, 2013, 10 : 189 - 199
[32] On the stability of periodic solutions of piecewise smooth periodic differential equations
Han, Maoan
Ye, Yan
ACTA MATHEMATICA SCIENTIA, 2024, 44 (04) : 1524 - 1535
[33] Stable periodic solutions in the forced pendulum equation
Ortega, Rafael
REGULAR & CHAOTIC DYNAMICS, 2013, 18 (06) : 585 - 599
[34] STABLE PERIODIC SOLUTIONS FOR NAZARENKO'S EQUATION
Beretka, Szandra
Vas, Gabriella
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2020, 19 (06) : 3257 - 3281
[35] SPATIAL HOMOGENEITY OF STABLE SOLUTIONS FOR ALMOST PERIODIC PARABOLIC EQUATIONS WITH VARIABLE DIFFUSION
Li, Hong-xu
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2024, : 2669 - 2683
[36] The periodic solutions of a stochastic chemostat model with periodic washout rate
Wang, Liang
Jiang, Daqing
O'Regan, Donal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2016, 37 : 1 - 13
[37] Stability properties of periodic solutions of a Duffing equation in the presence of lower and upper solutions
Njoku, FI
Omari, P
APPLIED MATHEMATICS AND COMPUTATION, 2003, 135 (2-3) : 471 - 490
[38] Multiplicity of periodic solutions of semilinear Duffing's equation at resonance
Wang, ZH
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1999, 237 (01) : 166 - 187
[39] THE PERIODIC SOLUTIONS OF CERTAIN EQUATIONS WITH PERIODIC COEFFICIENTS
林木仁
Annals of Differential Equations, 1998, (02) : 142 - 148
[40] Periodic solutions for evolution equations
Li, Y
Cong, FZ
Lin, ZH
Liu, WB
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 36 (03) : 275 - 293

← 1 2 3 4 5 →