Non-autonomous scalar discontinuous ordinary differential equation
type: Item
instance of: scholarly article
title: Non-autonomous scalar discontinuous ordinary differential equation
zbMATH Open document ID: 1083.34502
author: Piotr Pikuta
author: Witold Rzymowski
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-06-23T00:00:00Z
review text: A scalar differential equation is considered. The right-hand side of the equation represents a sum of a discontinuous function \(f(x)\) and a function \(h(t)\). The functions \(f\) and \(h\) are nonnegative, \(f\) is finite a.e. and \(1/f\) and \(h\) are Lebesgue integrable. The existence of a local absolutely continuous solution is proved. The authors make a mistake asserting that the problem in example 6 has only two solutions. In fact, the problem has an uncountable set of solutions.
reviewed by: A. A. Tolstonogov
Mathematics Subject Classification ID: 34A36
zbMATH DE Number: 2182078
zbMATH Keywords: discontinuous differential equations
MaRDI profile type: Publication
full work available at URL: j.jmaa.2005.02.013
OpenAlex ID: W2067772716
cites work: The differential equation x=fox
cites work: Existence of solutions for a class of discontinuous differential equations in \(\mathbb{R}^n\)
Wikidata QID: Q115346328
DOI: 10.1016/J.JMAA.2005.02.013
description: scientific article; zbMATH DE number 2182078