On Borel summation and Stokes phenomena for rank-\(1\) nonlinear systems of ordinary differential equations
type: Item
instance of: scholarly article
title: On Borel summation and Stokes phenomena for rank-\(1\) nonlinear systems of ordinary differential equations
zbMATH Open document ID: 0948.34068
DOI: 10.1215/S0012-7094-98-09311-5
author: O. Costin
published in: Duke Mathematical Journal
publication date: 2000-03-27T00:00:00Z
review text: The author studies in detail nonlinear systems of ordinary differential equations at an irregular singularity of rank 1, under nonresonance conditions. He shows that the formal asymptotic exponential series solutions are Borel summable in a generalized sense (i.e. in a sense in order that the summation is linear, multiplicative and commutes with differentiation and complex conjugation) along any direction in which the exponentials decay. The connection between local and classical Stokes phenomena is analyzed.
Mathematics Subject Classification ID: 34M40
Mathematics Subject Classification ID: 34M25
Mathematics Subject Classification ID: 34M37
zbMATH DE Number: 1425119
zbMATH Keywords: nonlinear systems of ordinary differential equations
zbMATH Keywords: irregular singularity
zbMATH Keywords: nonresonance conditions
zbMATH Keywords: local and classical Stokes phenomena
reviewed by: S. K. Chatterjea
MaRDI profile type: Publication
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full work available at URL: s0012-7094-98-09311-5
OpenAlex ID: W1985173721
description: scientific article; zbMATH DE number 1425119