On the integral curve of a linear third order O. D. E
type: Item
instance of: scholarly article
title: On the integral curve of a linear third order O. D. E
zbMATH Open document ID: 0946.34003
published in: Journal of Differential Equations
publication date: 1997-05-28T00:00:00Z
review text: The integral curves \(\gamma\) of the third-order linear differential equation \[ y'''+ 3p_1y''+ 3p_2y'+ p_3y= 0\tag{\(*\)} \] with smooth variable coefficients \(p_j\) is studied. Here, \(\gamma: \mathbb{R}\to \mathbb{R}\mathbb{P}^2\) is defined in homogeneous coordinates by \([y_1: y_2: y_3]\), where \(y_1\), \(y_2\), \(y_3\) are linearly independent solutions to \((*)\). A similar approach to the above-mentioned matter is used in the monography [\textit{F. Neuman}, Global properties of linear ordinary differential equations, Academia Praha and Dodrecht: Kluwer Academic Publishers (1991; Zbl 0784.34009)] and in papers, mentioned there. This fact is not mentioned by the author.
reviewed by: J.Vosmanský
Mathematics Subject Classification ID: 34A05
Mathematics Subject Classification ID: 34A26
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 1014436
zbMATH Keywords: integral curve
zbMATH Keywords: projective transformations
zbMATH Keywords: parametrizations
zbMATH Keywords: Wirtinger inequality
zbMATH Keywords: locally convex curves
author: Richard Evan Schwartz
MaRDI profile type: Publication
full work available at URL: jdeq.1996.3197
OpenAlex ID: W1978203066
cites work: Q5813619
cites work: A projectively natural flow for circle diffeomorphisms
DOI: 10.1006/JDEQ.1996.3197
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description: scientific article; zbMATH DE number 1014436