Linearization of boundary eigenvalue problems (Q1175048)

There are considered boundary eigenvalue problems of the form \(T_ 1(\lambda)f=g\), \(T_ 1(\lambda):=L-\lambda\), \(L\) ordinary differential operator in some Banach space and with boundary conditions \(T_ 2(\lambda)f=0\), depending holomorphically on \(\lambda\). Linearizations of such problems are studied using the theory of realizations of holomorphic operator functions and of operator colligations. The results are illustrated by two examples: the general regular \(\lambda\)-linear first order system on a compact interval with a two point boundary condition depending polynomically on \(\lambda\), a second order Sturm-Liouville problem on some interval with a \(\lambda\)- depending boundary condition.