Constructive proof of the existence of periodic solutions to the Duffing equation
type: Item
instance of: scholarly article
title: Constructive proof of the existence of periodic solutions to the Duffing equation
zbMATH Open document ID: 0910.34049
DOI: 10.1007/BF02882778
author: Weiguo Li
author: Zhue Shen
published in: Chinese Science Bulletin
publication date: 1999-04-08T00:00:00Z
review text: The authors consider the periodic boundary value problem \[ {c} x''(t) + Cx'(t) +g(t,x(t)) = e(t), \;t \in \mathbb{R}, \quad x(0) -x(2\pi) = x'(0) - x'(2\pi) = 0, \] where \(g\) is continuous, of class \(C^{1}\) with respect to \(x\) and \(2\pi\)-periodic with respect to \(t\), \(C\in \mathbb{R}\) and \(e\) is continuous and \(2\pi\)-periodic. Under a well-known additional assumption on \(g'_{x}(t,x)\), related to a suitable interaction of this function with the eigenvalues of the corresponding linear homogeneous problem, the authors provide a constructive proof of the existence of a unique \(2\pi\)-periodic solution to the previous problem, computing such solution. This result is illustrated with two graphical concrete examples.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 65L10
zbMATH DE Number: 1159107
zbMATH Keywords: Duffing equation
zbMATH Keywords: periodic solutions
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
zbMATH Keywords: constructive methods
zbMATH Keywords: numerical analysis
reviewed by: Antonio Cañada
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1159107