A class of linear partial neutral functional differential equations with nondense domain
type: Item
instance of: scholarly article
title: A class of linear partial neutral functional differential equations with nondense domain
zbMATH Open document ID: 0915.35109
author: Mostafa Adimy
author: Khalil Ezzinbi
published in: Journal of Differential Equations
publication date: 1999-07-07T00:00:00Z
review text: The paper deals with the linear neutral differential equations on a Banach space \(X\), \[ {d\over dt} (x(t)- Bx(t- h))= A_0x(t)+ Cx(t- h)+ L(x_t),\quad t\geq 0,\quad x(0)= \varphi\in C_X, \] where \(A_0: D(A_0)\subseteq X\mapsto X\) is a linear operator, \(B,C\in{\mathcal L}(X)\), \(L\) is a continuous linear functional from \(C_X:= C([-h,0],X)\) into \(X, \varphi\in C_X\) and \(x_t(\theta)= x(t+ \theta)\), \({-h\leq\theta\leq 0}\). A variation-of-constants formula is derived allowing transformation of integral solutions of the above problem to solutions of an abstract Volterra integral equation. The authors prove existence and uniqueness results and show that the solutions generate an integrated semigroup.
reviewed by: Drumi Bainov
Mathematics Subject Classification ID: 35R10
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35R15
zbMATH DE Number: 1212347
zbMATH Keywords: neutral partial functional differential equations
zbMATH Keywords: nondense domain
zbMATH Keywords: existence
zbMATH Keywords: uniqueness
MaRDI profile type: Publication
full work available at URL: jdeq.1998.3446
OpenAlex ID: W2026851688
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DOI: 10.1006/JDEQ.1998.3446
description: scientific article; zbMATH DE number 1212347