Bounded solutions of an abstract differential equation of special form with delayed argument
type: Item
instance of: scholarly article
title: Bounded solutions of an abstract differential equation of special form with delayed argument
zbMATH Open document ID: 1291.34123
author: Yu. V. Il'chenko
published in: Journal of Mathematical Sciences (New York)
publication date: 2013-04-24T00:00:00Z
review text: The differential equation with delayed argument \[ x^\prime(t) = A_1 x(t) + A_2 x(t-1)+y(t),\quad t\in \mathbb{R} \] is considered, where the unknown function \(x\) maps \(\mathbb{R}\) into a complex Banach space. There are two results which establish necessary conditions for the existence and uniqueness of a bounded solution with bounded derivative.
reviewed by: Andrei Horvat-Marc
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K12
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 6157080
zbMATH Keywords: differential equation with delay
zbMATH Keywords: bounded solution
MaRDI profile type: Publication
full work available at URL: s10958-012-1074-y
OpenAlex ID: W1994917234
Wikidata QID: Q115382383
cites work: On the existence and uniqueness of a bounded solution to a linear differential equation with shifts of argument in Banach space
cites work: Functions of shift operator and their applications to difference equations
DOI: 10.1007/S10958-012-1074-Y
description: scientific article; zbMATH DE number 6157080