Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 146, pp. 121.
Linear secondorder problems with SturmLiouvilletype multipoint
boundary conditions
Bryan P. Rynne
Abstract:
We consider the eigenvalue problem for the equation
on
,
together with general SturmLiouvilletype, multipoint boundary
conditions at
.
We show that the basic spectral properties of this problem are similar
to those of the standard SturmLiouville problem with separated boundary
conditions.
In particular, for each integer
there exists a unique, simple
eigenvalue
whose eigenfunctions have 'oscillation count'
equal to k.
Similar multipoint problems have been considered before
for Dirichlettype or Neumanntype multipoint boundary
conditions, or a mixture of these.
Different oscillation counting methods have been used in each of these
cases. A new oscillation counting method is used here which unifies and
extends all the results for these special case to the general
SturmLiouvilletype boundary conditions.
Submitted October 28, 2011. Published August 21, 2012.
Math Subject Classifications: 34B05, 34B10, 34B24, 34B25.
Key Words: Second order ordinary differential equations;
multipoint boundary conditions; SturmLiouville problems.
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Bryan P. Rynne
Department of Mathematics and the
Maxwell Institute for Mathematical Sciences
HeriotWatt University
Edinburgh EH14 4AS, Scotland
email: bryan@ma.hw.ac.uk

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