Ein ailgemeines Bifurkationstheorem

  • Eberhard Zeidler

    Mathematik in den Naturwissenschaften, Leipzig, Germany


We prove a general bifurcation theorem. Using generic bifurcation conditions, we select a set of normalized elements in the null space of the linearized operator. From each element of 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.

Cite this article

Eberhard Zeidler, Ein ailgemeines Bifurkationstheorem. Z. Anal. Anwend. 4 (1985), no. 5, pp. 403–411

DOI 10.4171/ZAA/162