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Zeitschrift für Analysis und ihre Anwendungen

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Volume 4, Issue 5, 1985, pp. 403–411
DOI: 10.4171/ZAA/162

Published online: 1985-10-31

Ein ailgemeines Bifurkationstheorem

Eberhard Zeidler[1]

(1) Mathematik in den Naturwissenschaften, Leipzig, Germany

We prove a general bifurcation theorem. Using generic bifurcation conditions, we select a set $B$ of normalized elements in the null space of the linearized operator. From each element of $B$ there bifurcates exactly one solution branch of the given nonlinear operator equation. Moreover, we can construct the branches by a convergent iterative method. The theorem allows a variety of interesting applications, e.g., to free boundary value problems in the theory of ideal fluids, to Taylor’s problem and Bénard’s problem in the framework of the Navier-Stokes equations, and to Hopf bifurcation.

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Zeidler Eberhard: Ein ailgemeines Bifurkationstheorem. Z. Anal. Anwend. 4 (1985), 403-411. doi: 10.4171/ZAA/162