A Picard method without Lipschitz continuity for some ordinary differential equations
type: Item
instance of: scholarly article
title: A Picard method without Lipschitz continuity for some ordinary differential equations
zbMATH Open document ID: 0890.34002
author: Francisco Bernis
author: Man Kam Kwong
published in: Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI
publication date: 1998-06-09T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/73395
review text: Consider an initial value problem to the scalar differential equation \(y^{(m)} (x)= f(x,y)\) where \(f\) may fail to be Lipschitzian in \(y\) or even to be continuous. The author derives conditions on \(f\) (which imply e.g. a certain asymptotic behavior in \(x\)) such that existence and uniqueness can be proved by means of a modified Picard iteration.
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 1051566
zbMATH Keywords: initial value problem
zbMATH Keywords: scalar differential equation
zbMATH Keywords: modified Picard iteration
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
OpenAlex ID: W2321900711
cites work: Q4274968
cites work: Similarity solutions of a higher order nonlinear diffusion equation
cites work: Q3933274
cites work: Uniqueness for a class of nonlinear initial value problems
cites work: Uniqueness results for some nonlinear initial and boundary value problems
DOI: 10.5802/AFST.840
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description: scientific article; zbMATH DE number 1051566