Lagrange stability for asymmetric Duffing equations
type: Item
instance of: scholarly article
title: Lagrange stability for asymmetric Duffing equations
zbMATH Open document ID: 0970.37045
DOI: 10.1016/S0362-546X(99)00170-4
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2001-04-19T00:00:00Z
review text: For the Duffing equation \(\frac{d^2x}{d^2t}+g(x)=e(t)\) where \(e(t)\) is of period 1 and \(g(x)\text{sgn }x\rightarrow +\infty \) as \(x\rightarrow \pm \infty\) let us associate \(a=\lim_{x \to -\infty } \frac{g(x)}{x}\) and \(b=\lim_{x \to +\infty } \frac{g(x)}{x}\). Using Moser's twist theorem, the Lagrange stability in the cases \(-\infty <a<+\infty\), \(b=+\infty\) and \(-\infty <b<+\infty\), \(a=-\infty\) is studied.
Mathematics Subject Classification ID: 37J25
Mathematics Subject Classification ID: 70K20
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 1545346
zbMATH Keywords: Duffing equation
zbMATH Keywords: Lagrange stability
zbMATH Keywords: Moser's twist theorem
author: Xiaoping Yuan
reviewed by: Mircea Crasmareanu
MaRDI profile type: Publication
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full work available at URL: s0362-546x(99)00170-4
OpenAlex ID: W2062728263
description: scientific article; zbMATH DE number 1545346