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

$\displaystyle -y''+(q-\lambda-\frac{w}{u-\lambda})y=0
$

on the interval $ [0,1]$ with Dirichlet boundary conditions, where $ q$, $ u$, and $ w$ are real functions. If $ u$ is piece-wise continuous, then in every gap of the range of $ u$ 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

Gregynog Abstracts