Abstract
This paper is concerned with the existence of critical points for a functional f defined on the level set of a second functional g. Existence of nontrivial solutions for the nonlinear eigenvalue-problem f′(u) = λg′(u) and convergence for a nonlinear analogue to the Rayleigh-Ritz-Method is proven. The results are applied to a nonlinear ordinary eigenvalue problem where it is shown that the lowest point in the continuous spectrum of the associated linearized operator is a bifurcation point of infinite multiplicity.
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© 1980 Springer Basel AG
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Bongers, A. (1980). Ober Ein Rayleigh-Ritz-Verfahren zur Bestimmung Kritischer Werte. In: Mittelmann, H.D., Weber, H. (eds) Bifurcation Problems and their Numerical Solution. ISNM: International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 54. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6294-3_3
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DOI: https://doi.org/10.1007/978-3-0348-6294-3_3
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1204-6
Online ISBN: 978-3-0348-6294-3
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