A STURM-LIOUVILLE PROBLEM DEPENDING RATIONALLY ON THE EIGENVALUE PARAMETER

MATTHIAS LANGER

mlanger@math.uni-bremen.de

FB 3 - Mathematik
Universität Bremen
Bibliothekstrasse 1
D-28359 Bremen, Germany

We consider eigenvalues of the following Sturm-Liouville problem

on the interval with Dirichlet boundary conditions, where , , and are real functions. If is piece-wise continuous, then in every gap of the range of the eigenvalues can be characterised by a varitional principle with an index shift. The behaviour at the end-points of the gaps and the number of eigenvules are investigated.

EPSRC Gregynog Workshop, 21-26 July 2002