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Ordinary Differential Equations in Algebras of Generalized Functions

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Pseudo-Differential Operators, Generalized Functions and Asymptotics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 231))

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.

Mathematics Subject Classification (2010). Primary: 34A12, 46F30.

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Author information

Authors and Affiliations

  1. Institute for Statistics and Mathematics, Vienna University of Economics and Business, Augasse 2–6, A-1090, Vienna, Austria

    Evelina Erlacher

  2. Faculty of Mathematics, University of Vienna, Nordbergstr. 15, A-1090, Vienna, Austria

    Michael Grosser

Authors
  1. Evelina Erlacher
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  2. Michael Grosser
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Corresponding author

Correspondence to Evelina Erlacher .

Editor information

Editors and Affiliations

  1. , Department of Mathematics and Statistics, Queen's University, University Avenue, Jeffery Hall, Kingston, K7L 3N6, Ontario, Canada

    Shahla Molahajloo

  2. , Dept. of Mathematics & Informatics, University of Novi Sad, Trg Dsiteja Obradovica 4, Novi Sad, 21000, Serbia

    Stevan Pilipović

  3. Dept. of Computer Science, Physics, and Mathematics, Linnæus University, Vejdes Plats 6, Växjö, 351 95, Sweden

    Joachim Toft

  4. Department of Mathematics & Statistics, York University, Keele Street 4700, Toronto, M3J 1P3, Ontario, Canada

    M. W. Wong

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Erlacher, E., Grosser, M. (2013). Ordinary Differential Equations in Algebras of Generalized Functions. In: Molahajloo, S., Pilipović, S., Toft, J., Wong, M. (eds) Pseudo-Differential Operators, Generalized Functions and Asymptotics. Operator Theory: Advances and Applications, vol 231. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0585-8_13

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