How to define singular solutions
type: Item
instance of: scholarly article
title: How to define singular solutions
zbMATH Open document ID: 0794.34003
author: Jianming Yu
author: Shyuichi Izumiya
published in: Kodai Mathematical Journal
publication date: 1994-08-29T00:00:00Z
review text: Because implicit first order differential equations may have two- parameter families of solutions, the notions of ``general solution'' and ``singular solution'' as sometimes described in elementary texts are not appropriate. The authors use the ideas of contact geometry to give rigorous definitions, improving on an earlier approach by \textit{M. T. Fukuda} [Yokohama Math. J. 25, 41-58 (1977; Zbl 0372.34026)]. The approach is elementary and the main results can be extended to partial differential equations.
Mathematics Subject Classification ID: 34A09
Mathematics Subject Classification ID: 34A26
zbMATH DE Number: 515594
zbMATH Keywords: general solution
zbMATH Keywords: singular solution
zbMATH Keywords: implicit first order differential equations
zbMATH Keywords: contact geometry
reviewed by: Fred Brauer
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1138039786
OpenAlex ID: W2104164316
cites work: Q5345182
cites work: Q3280274
cites work: Q4150032
cites work: Q5843703
cites work: Singular Solutions of First-Order Differential Equations
DOI: 10.2996/KMJ/1138039786
description: scientific article; zbMATH DE number 515594