Singular differential equations with delay
type: Item
instance of: scholarly article
title: Singular differential equations with delay
zbMATH Open document ID: 1022.35080
author: Angelo Favini
author: Luciano Pandolfi
author: Hiroki Tanabe
published in: Differential and Integral Equations
publication date: 2003-01-26T00:00:00Z
review text: The authors study the initial value problem \[ d/dt(Mu(t))=-Lu(t)+L_1u(t-1),\quad t\geq 0,\qquad u(t)=\phi (t),\quad t\in [- 1,0] \] where \(M,L,L_1\) are closed linear operators in a Banach space \(X\), \(L\) is invertible and \(T=ML^{-1}\in L(X)\). They show existence of strict solutions provided \(z=0\) is a simple pole of \((z+T)^{-1}\) and \(\phi \) satisfies a compatibility condition. In the case of a reflexive Banach space, the pole hypotheses is relaxed. The theorems extend a class of operators for which existence results hold analogous to those for regular equation with \(M=I\). A variant of the variation of parameters formula is given as well as applications to concrete equations.
reviewed by: Hana Petzeltová
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 1858751
zbMATH Keywords: singular differential equation
zbMATH Keywords: delay equation
zbMATH Keywords: strict solutions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1858751