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Dynamics of Infinite Dimensional Systems pp 57–60Cite as

On Bifurcation for Variational Problems

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Part of the book series: NATO ASI Series ((NATO ASI F,volume 37))

Abstract

In this lecture we would like to present a bifurcation theorem for problems having a variational structure. It generalizes earlier results by Rabinowitz [5], Böhme [1] and Marino [4]. If one combines our result with a recent result of Maddocks [3] one can discuss global stability assignments for a given branch of solutions. Before we present our theorem in section II, we want to describe this application to stability analysis. Further applications to problems in mathematical physics may be found in Maddocks’ paper [3].

Research partially supported by National Science Foundation Grant DMS 8401719.

Supported by Deutsche Forschungsgemeinschaft LA 525/1-1.

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Bibliography

  1. Böhme, R.: Die Losung der Verzweigungsgleichung fur nicht-Lineare Eigenwertprobleme, Math. Z. 27 (1972), 105–126.

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  2. Chow, S.-N. and Lauterbach, R.: A Bifurcation Theorem for Critical Points of Variational Problems, Preprint 1985.

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  3. Maddocks, J.: Preprint 1985.

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  4. Marino, A.: La biforcazione nel caso variationale, Conf. Sem. Mat. Bari 1973.

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  5. Rabinowitz, P.H.: A bifurcation theorem for potential operators, J. Funct. Anal. 25 (1977), 412–424.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Michigan State University, Wells Hall, East Lansing, MI, 48824, USA

    Shui-Nee Chow

  2. Institut für Mathematik, Universität Augsburg, Memminger Str. 6, D-89, Augsburg, West Germany

    Reiner Lauterbach

Authors
  1. Shui-Nee Chow
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  2. Reiner Lauterbach
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824-1027, East Lansing, MI, USA

    Shui-Nee Chow

  2. Division of Applied Mathematics, Brown University, 02912, Providence, RI, USA

    Jack K. Hale

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© 1987 Springer-Verlag Berlin Heidelberg

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Chow, SN., Lauterbach, R. (1987). On Bifurcation for Variational Problems. In: Chow, SN., Hale, J.K. (eds) Dynamics of Infinite Dimensional Systems. NATO ASI Series, vol 37. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-86458-2_7

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  • DOI: https://doi.org/10.1007/978-3-642-86458-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-86460-5

  • Online ISBN: 978-3-642-86458-2

  • eBook Packages: Springer Book Archive

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