Semistable operators and singularly perturbed differential equations
type: Item
instance of: scholarly article
title: Semistable operators and singularly perturbed differential equations
zbMATH Open document ID: 0928.47009
author: J. J. Koliha
author: Trung Dinh Tran
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-04-13T00:00:00Z
review text: The purpose of the paper is to prove the existence of \(\lim_{s\to\infty} \exp(sA+B)\) where \(A\), \(B\) are bounded linear operators in a Banach space \(X\) and \(A\) is semistable (i.e., if \(\sigma(A)\) denotes the spectrum of \(A\) and \(H^-\) denotes the open left half-plane of the complex plane \(\mathbb{C}\), then \(\sigma(A)\subset H^-\cup\{0\}\), where \(0\) is at most a simple pole of \(A\)). The proof is based on the upper semicontinuity of the spectrum and on a uniform perturbation result for resolvents. Some applications to differential equations are given.
Mathematics Subject Classification ID: 47A60
Mathematics Subject Classification ID: 47E05
Mathematics Subject Classification ID: 47A55
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 47A10
zbMATH DE Number: 1274900
zbMATH Keywords: semistable operator
zbMATH Keywords: perturbed differential equation
zbMATH Keywords: upper semicontinuity of the spectrum
zbMATH Keywords: resolvents
zbMATH Keywords: differential equations
reviewed by: Svatoslav Staněk
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6235
OpenAlex ID: W2068648489
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DOI: 10.1006/JMAA.1998.6235
description: scientific article; zbMATH DE number 1274900