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Title: Closed semistable operators and singular differential equations (English)
Author: Koliha, J. J.
Author: Tran, Trung Dinh
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 3
Year: 2003
Pages: 605-620
Summary lang: English
Category: math
Summary: We study a class of closed linear operators on a Banach space whose nonzero spectrum lies in the open left half plane, and for which $0$ is at most a simple pole of the operator resolvent. Our spectral theory based methods enable us to give a simple proof of the characterization of $C_0$-semigroups of bounded linear operators with asynchronous exponential growth, and recover results of Thieme, Webb and van Neerven. The results are applied to the study of the asymptotic behavior of the solutions to a singularly perturbed differential equation in a Banach space. (English)
Keyword: closed linear operator
Keyword: $C_0$-semigroup
Keyword: infinitesimal generator
Keyword: semistable operator
Keyword: singular differential equation
MSC: 34G10
MSC: 47A10
MSC: 47A60
MSC: 47D06
idZBL: Zbl 1080.47500
idMR: MR2000056
Date available: 2009-09-24T11:04:54Z
Last updated: 2020-07-03
Stable URL:
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