On solvability of degenerate nonstationary differential-difference equations in Banach spaces
type: Item
instance of: scholarly article
title: On solvability of degenerate nonstationary differential-difference equations in Banach spaces
zbMATH Open document ID: 1017.35112
author: Angelo Favini
author: L. A. Vlasenko
published in: Differential and Integral Equations
publication date: 2003-03-13T00:00:00Z
review text: The authors study the following differential problem \[ A(t)u^\prime (t) + B(t)u(t) + M(t)u^\prime (t-\omega) + N(t)u(t-\omega)=f(t), \quad t \in J \subset\mathbb{R}, \] \[ u(t) = g(t),\qquad - \omega \leq t \leq 0, \] where the operators \(A(t), B(t), M(t), N(t) (t \in J)\) are closed linear operators from a Banach space \(X\) into a Banach space \(Y\) and the operator \(A(t)\) is not supposed to be invertible. The problem is studied in the case when the point \(\mu = 0\) is a simple pole of the resolvent operator \((\mu B(t) + A(t))^{-1}\) for all \(t \in J\). The authors also consider the case of stationary operators \(A,B\) when the resolvent \((\mu B + A)^{-1}\) has a multiple pole at \(\mu = 0\). Concrete applications to partial differential equations with delay are given.
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35K65
Mathematics Subject Classification ID: 35G10
Mathematics Subject Classification ID: 35K25
Mathematics Subject Classification ID: 34G10
zbMATH DE Number: 1832847
zbMATH Keywords: differential-difference equations
zbMATH Keywords: Banach spaces
zbMATH Keywords: partial differential equations with delay
reviewed by: Emil Minchev
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1832847