On complete second order linear differential equations in Banach spaces
type: Item
instance of: scholarly article
title: On complete second order linear differential equations in Banach spaces
zbMATH Open document ID: 0663.34053
author: Tijun Xio
author: Jin Liang
published in: Pacific Journal of Mathematics
publication date: 1990-01-01T00:00:00Z
review text: The authors deal with the equation \(u''(t)+Bu'(t)+Au(t)=0\) \((t\geq 0)\) in a Banach space \(E\) where \(A, B\) are densely defined closed linear operators. Their main results are two necessary and sufficient conditions on \(A\), \(B\) for strong well posedness of the Cauchy problem. Moreover, they give explicit expressions for the propagators C(.), S(.), generalize some results in the case D(A)\(\supseteq D(B)\), and exhibit a partial differential equation.
reviewed by: E.Barvinek
Mathematics Subject Classification ID: 34G10
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 4084122
zbMATH Keywords: Banach space
zbMATH Keywords: densely defined closed linear operators
zbMATH Keywords: Cauchy problem
MaRDI profile type: Publication
full work available at URL: pjm.1990.142.175
OpenAlex ID: W2081721226
DOI: 10.2140/PJM.1990.142.175
description: scientific article; zbMATH DE number 4084122