Ordinary Differential Equations in Algebras of Generalized Functions

Evelina Erlacher; Michael Grosser

doi:10.1007/978-3-0348-0585-8_13

Ordinary Differential Equations in Algebras of Generalized Functions

Evelina Erlacher, Michael Grosser

Statistics and Mathematics

Publikation: Wissenschaftliche Fachzeitschrift › Originalbeitrag in Fachzeitschrift › Begutachtung

Abstract

A local existence and uniqueness theorem for ODEs in the special algebra of generalized functions is established, as well as versions including parameters and dependence on initial values in the generalized sense. Finally, a Frobenius theorem is proved. In all these results, composition of generalized functions is based on the notion of c-boundedness.

Originalsprache	Englisch
Seiten (von - bis)	253 - 270
Fachzeitschrift	Operator Theory: Advances and Applications
Jahrgang	231
DOIs	https://doi.org/10.1007/978-3-0348-0585-8_13
Publikationsstatus	Veröffentlicht - 1 Dez. 2013

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AB - A local existence and uniqueness theorem for ODEs in the special algebra of generalized functions is established, as well as versions including parameters and dependence on initial values in the generalized sense. Finally, a Frobenius theorem is proved. In all these results, composition of generalized functions is based on the notion of c-boundedness.

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