Parameter-dependent linear ordinary differential equations and topology of domains

The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or characterizations of such sets via nonvanishing Wronskians are sensiti...

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Bibliographic Details
Published inarXiv.org
Main Authors Boyko, Vyacheslav M, Kunzinger, Michael, Popovych, Roman O
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.03.2021
Subjects
Differential equations
Domains
Independent variables
Mathematical analysis
Mathematics - Classical Analysis and ODEs
Ordinary differential equations
Parameters
Properties (attributes)
Topology
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Summary:The well-known solution theory for (systems of) linear ordinary differential equations undergoes significant changes when introducing an additional real parameter. Properties like the existence of fundamental sets of solutions or characterizations of such sets via nonvanishing Wronskians are sensitive to the topological properties of the underlying domain of the independent variable and the parameter. We give a complete characterization of the solvability of such parameter-dependent equations and systems in terms of topological properties of the domain. In addition, we also investigate this problem in the setting of Schwartz distributions.
ISSN:2331-8422
DOI:10.48550/arxiv.1901.02059