The twist coefficient of periodic solutions of a time-dependent Newton's equation
type: Item
instance of: scholarly article
title: The twist coefficient of periodic solutions of a time-dependent Newton's equation
zbMATH Open document ID: 0761.34036
DOI: 10.1007/BF01048263
published in: Journal of Dynamics and Differential Equations
publication date: 1993-01-17T00:00:00Z
review text: A \(T\)-periodic solution \(\varphi\) of a \(T\)-periodic equation \(x''+f(t,x)=0\) is considered. It is supposed that \(\varphi\) is generic non zero twist type up to the 4th order terms. If \(f(t,x)=a(t)x+b(t)x^ 2+c(t)x^ 3+\dots\) and \(\varphi(t)\equiv 0\) then conditions for the coefficients (boundedness and sign type) are formulated, which guarantee that the trivial solution is of twist type and as a consequence Lyapunov stable. The results are illustrated by examples including the pendulum of variable length.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 96102
zbMATH Keywords: \(T\)-periodic solution
zbMATH Keywords: twist type
zbMATH Keywords: Lyapunov stable
zbMATH Keywords: examples
zbMATH Keywords: pendulum of variable length
Wikidata QID: Q115394566
author: Rafael Ortega
reviewed by: Péter F. Moson
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 96102