Ein selektives Projektions-Iterationsverfahren und Anwendungen auf Verzweigungsprobleme

In the present paper a projection-iteration procedure for solving nonlinear operator-equations is described in abstract spaces. The method possesses a selection property by yielding only those solutions which have certain stability properties. Parameter-dependent equations and bifurcation problems are considered as well. It is shown that in the case of bifurcation near a simple eigenvalue, the method converges locally always to the "stable" solution except for initial values on a proper submanifold. Numerical results for a nonlinear boundary-value problem are given illustrating this selection character.