Entire solutions of higher order abstract Cauchy problems
type: Item
instance of: scholarly article
title: Entire solutions of higher order abstract Cauchy problems
zbMATH Open document ID: 0879.34062
author: Jin Liang
author: Ti-Jun Xiao
published in: Journal of Mathematical Analysis and Applications
publication date: 1998-01-29T00:00:00Z
review text: The abstract Cauchy problem for the higher order differential equation \[ u^{(n)} (t)+ \sum^{n-1}_{i=0} A_ju^{(j)} (t)=0,\;t\geq 0;\;u^{(j)} (0)= u_j,\;0\leq j\leq n-1 \tag{1} \] is considered. The operators \(A_0\), \(A_1, \dots, A_{n-1}\) are closed linear operators with ranges and domains contained in a suitable complex Banach space \(E\). The concept of the entire solution of (1) is introduced and its existence and uniqueness is investigated. In particular, some conditions ensuring that (1) has a unique entire solution for every initial datum in a dense set are found. These conditions are satisfied for parabolic higher order linear differential equations.
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 47D06
zbMATH DE Number: 1031573
zbMATH Keywords: abstract Cauchy problem
zbMATH Keywords: higher order differential equation
zbMATH Keywords: entire solution
zbMATH Keywords: parabolic higher order linear differential equations
reviewed by: S. Totaro
MaRDI profile type: Publication
full work available at URL: jmaa.1997.5266
OpenAlex ID: W1981170838
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DOI: 10.1006/JMAA.1997.5266
description: scientific article; zbMATH DE number 1031573