Differential equations for which the cross-ratio of four solutions is weakly monotone
type: Item
instance of: scholarly article
title: Differential equations for which the cross-ratio of four solutions is weakly monotone
zbMATH Open document ID: 0858.34030
author: Kurt Munk Andersen
author: Allan Sandqvist
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-09-30T00:00:00Z
review text: A Riccati equation is a scalar differential equation \(x'=f(t,x)\) for which the derivative of \(f\) with respect to \(x\) is linear in \(x\). It is well-known that the cross ratio of any four distinct solutions of a Riccati equation is constant. In this paper, the authors prove that the derivative of \(f\) with respect to \(x\) is weakly convex (resp. concave) if and only if the cross ratio of any four solutions \(x(t)<y(t)<u(t)<v(t)\) is weakly increasing (resp. decreasing).
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 930183
zbMATH Keywords: Riccati equation
zbMATH Keywords: cross ratio of any four distinct solutions
reviewed by: M. Farkas
MaRDI profile type: Publication
full work available at URL: jmaa.1996.0275
OpenAlex ID: W1981781979
DOI: 10.1006/JMAA.1996.0275
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description: scientific article; zbMATH DE number 930183