Abstract

On $\lambda$--nonlinear boundary eigenvalue problems C. Tretter In this lecture nonselfadjoint boundary eigenvalue problems for ordinary differential equations $N(y) = \lambda P(y)$ where ord $N>$ ord $P$ with $\lambda$--polynomial boundary conditions are considered. A linearization is presented which is itself a boundary eigenvalue problem, namely a first order system of differential equations with $\lambda$--linear boundary conditions. For regular problems of this type completeness, minimality and basis results for the eigenfunctions and associated functions are presented. Via the linearization results for the eigenfunctions and associated functions of the original $\lambda$--polynomial boundary eigenvalue problems are obtained.

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