A note on blow-up solutions for a scalar differential equation with a discrete delay
type: Item
instance of: scholarly article
title: A note on blow-up solutions for a scalar differential equation with a discrete delay
author: Tetsuya Ishiwata
author: Yukihiko Nakata
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 2022-12-01T00:00:00Z
review text: In this note, blow-up solutions of delay differential equations (DDE) of the form \(\frac{dx}{dt} = F(x(t), x(t-1))\) are considered. It is proved that if there exists \(a\in\mathbb{R}\) such that the ordinary differential equation (ODE) \(\frac{dx}{dt} = F(x(t), a)\) has a blow-up solution, then the DDE has blow-up solutions. Conversely, it is also proved that, under certain conditions on \(F\), if the DDE has a blow-up solution, then there exists \(a\in\mathbb{R}\) such that the ODE has blow-up solutions. Various particular cases with examples are also provided to demonstrate the main results and remark points.
reviewed by: Zhanyuan Hou
Mathematics Subject Classification ID: 34K12
zbMATH DE Number: 7625959
zbMATH Keywords: delay differential equations
zbMATH Keywords: blow-up solutions
zbMATH Keywords: delay-induced blow-up
MaRDI profile type: Publication
full work available at URL: s13160-022-00533-y
OpenAlex ID: W4294053789
Wikidata QID: Q113899366
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DOI: 10.1007/S13160-022-00533-Y
description: scientific article; zbMATH DE number 7625959