Ein ailgemeines Bifurkationstheorem

Abstract

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.