Electron. J. Diff. Equ., Vol. 2012 (2012), No. 123, pp. 1-13.

Sturm-Liouville eigenvalue characterizations

Paul B. Bailey, Anton Zettl

We study the relationship between the eigenvalues of separated self-adjoint boundary conditions and coupled self-adjoint conditions. Given an arbitrary real coupled boundary condition determined by a coupling matrix K we construct a one parameter family of separated conditions and show that all the eigenvalues for K and -K are extrema of the eigencurves of this family. This characterization makes it possible to use the well known Prufer transformation which has been used very successfully, both theoretically and numerically, for separated conditions, also in the coupled case. In particular, this characterization makes it possible to compute the eigenvalues for any real coupled self-adjoint boundary condition using any code which works for separated conditions.

Submitted June 4, 2012. Published July 23, 2012.
Math Subject Classifications: 05C38, 15A15, 05A15, 15A18
Key Words: Sturm-Liouville problems; computing eigenvalues; separated and coupled boundary conditions.

Show me the PDF file (252 KB), TEX file, and other files for this article.

Paul B. Bailey
10950 N. La Canada Dr., #5107
Tucson, AZ 85737, USA
email: paulbailey10950@comcast.net
Anton Zettl
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL 60155, USA
email: zettl@math.niu.edu

Return to the EJDE web page