Uniqueness of Local, Analytic Solutions to Singular ODEs-Reference-Cited by-同舟云学术

Uniqueness of Local, Analytic Solutions to Singular ODEs

Published:2022-07-12 Issue:1 Volume:180 Page:
ISSN:0167-8019
Container-title:Acta Applicandae Mathematicae
language:en
Short-container-title:Acta Appl Math

Author:

de Jong Thomas Geert^ORCID,van Meurs Patrick

Abstract

AbstractWe study local, analytic solutions for a class of initial value problems for singular ODEs. We prove existence and uniqueness of such solutions under a certain non-resonance condition. Our proof translates the singular initial value problem to an equilibrium problem of a regular ODE. Then, we apply classical invariant manifold theory. We demonstrate that the class of ODEs under consideration captures models which describe the shape of axially symmetric surfaces which are closed on one side. Our main result guarantees smoothness at the tip of the surface.

Funder

Japan Society for the Promotion of Science

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics

Link

https://link.springer.com/content/pdf/10.1007/s10440-022-00517-7.pdf

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