Periodic solutions of discontinuous damped Duffing equations
type: Item
instance of: scholarly article
title: Periodic solutions of discontinuous damped Duffing equations
zbMATH Open document ID: 1412.34064
author: Fangfang Jiang
author: Zhicheng Ji
author: Yan Wang
published in: Nonlinear Analysis. Real World Applications
publication date: 2019-02-27T00:00:00Z
review text: In this paper, the authors study the following damped Duffing equation with a line of discontinuity \[ x''+cx'+g(x)=e(t),\quad x\in \mathbb{R},\tag{1} \] where \(x'\triangleq \frac{dx}{dt} \) and \(x''\triangleq \frac{d^2x}{dt^2},\) \(c>0\) is a constant, \(g(x)\) is given by \[ g(x)=\begin{cases} g_+(x), & x > 0, \\ g_-(x), & x < 0, \end{cases} \] \(e \in C^0(\mathbb{R},\mathbb{R})\) satisfying \(e(t + T) = e(t)\) and \(T > 0\) is the minimum period. Firstly, they prove that the periodic solutions of equation (1) can only be harmonic and subharmonic solutions. Secondly, the geometric properties of solutions for equation (1) are given. Finally, by using the two-dimension Poincaré-Bohl theorem, they obtain the existence and uniqueness of crossing harmonic and subharmonic solutions of equation (1).
reviewed by: Chun Li
Mathematics Subject Classification ID: 34A36
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 7030198
zbMATH Keywords: discontinuity
zbMATH Keywords: damping
zbMATH Keywords: harmonic and subharmonic solutions
zbMATH Keywords: Poincaré-Bohl theorem
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2018.11.009
OpenAlex ID: W2906707885
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Wikidata QID: Q128610950
DOI: 10.1016/J.NONRWA.2018.11.009
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description: scientific article; zbMATH DE number 7030198