Constructive branching theory for semi-eigenvalues

By linearization of nonlinear semi-eigenvalue problems, especially for anal ytic maps with completely continuous Frechet derivative, we develop the (pr imary) branching solutions and the corresponding semi-eigenvalues into powe r series with respect to a real parameter. We consider the algebraically si mple case of the semi-eigenvalue of the linearization using the implicit fu nction theorem and the Fredholm alternative.