Singular perturbation of linear systems with a regular singularity
type: Item
instance of: scholarly article
title: Singular perturbation of linear systems with a regular singularity
zbMATH Open document ID: 1020.34085
DOI: 10.1023/A:1016326320001
author: Werner Balser
author: Vladimir P. Kostov
published in: Journal of Dynamical and Control Systems
publication date: 2002-12-15T00:00:00Z
review text: The paper is devoted to the study of singularly perturbed inhomogeneous linear systems of the form \[ \varepsilon zx'= A(z,\varepsilon) x- f(z,\varepsilon), \] having a regular singularity at the origin. Summability properties of the unique formal solution, which is a power series with respect to the variable \(z\) and the perturbation parameter \(\varepsilon\), are investigated. Finally, it is shown that the series, regarded as a power series in \(\varepsilon\) with coefficients depending on \(z\), is 1-summable under a suitable and sharp eigenvalue condition.
Mathematics Subject Classification ID: 34M30
Mathematics Subject Classification ID: 34M60
zbMATH DE Number: 1845279
zbMATH Keywords: regular singularity
zbMATH Keywords: singular perturbation
zbMATH Keywords: 1-summability
reviewed by: J. Saurer
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1845279