Konstruktive Verzweigungstheorie für Halbeigenwerte

Abstract

By linearization of nonlinear semi-eigenvalue problem, especially for analytic maps with completely continuous Fréchet derivative, we develop the (primary) branching solutions and the corresponding semi-cigenvalues into power series with respect to a real parameter. We consider the algebraically simple case of the semi-eigenvalue of the linearization using the implicit function theorem and the Fredholm alternative.