Scalar autonomous second order ordinary differential equations
type: Item
instance of: scholarly article
title: Scalar autonomous second order ordinary differential equations
zbMATH Open document ID: 1270.34080
author: C. Ragazzo
published in: Qualitative Theory of Dynamical Systems
publication date: 2013-04-05T00:00:00Z
review text: This paper deals with differential equations of the form \[ \begin{aligned} &\dot u = v,\\ &\dot v = F(u,v), \end{aligned} \] whereby \((u,v)\in{\mathbb R}^2\) and \(F\) an infinitely often differentiable function. The author's main concern, in the case when \(F(u,-v)=F(u,v)\), is to provide conditions so that there exist an infinitely often differentiable change of coordinates in \({\mathbb R}^2\), \((u,v)\mapsto (x,y)\) that transforms the above equation into \[ \begin{aligned} &\dot x = y,\\ &\dot y = g(x), \end{aligned} \] for an appropriate function \(g\).
reviewed by: Marco Spadini
Mathematics Subject Classification ID: 34C20
Mathematics Subject Classification ID: 34C41
zbMATH DE Number: 6150881
zbMATH Keywords: second order differential equations
zbMATH Keywords: change of variables
zbMATH Keywords: Abel function
MaRDI profile type: Publication
full work available at URL: s12346-011-0063-8
OpenAlex ID: W2012305391
Wikidata QID: Q121450379
Wikidata QID: Q121450391
Wikidata QID: Q121450455
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DOI: 10.1007/S12346-011-0063-8
description: scientific article; zbMATH DE number 6150881