Geodesic
Sturm-Liouville eigenvalue characterizations
Electronic Journal of Differential Equations, Tome 2012 (2012).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 05C38, 15A15, 05A15, 15A18
Keywords: Sturm-Liouville problems, computing eigenvalues, separated and coupled boundary conditions 
@article{EJDE_2012__2012__a72,
     author = {Bailey, Paul B. and Zettl, Anton},
     title = {Sturm-Liouville eigenvalue characterizations},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2012},
     year = {2012},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a72/}
}
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Bailey, Paul B.; Zettl, Anton. Sturm-Liouville eigenvalue characterizations. Electronic Journal of Differential Equations, Tome 2012 (2012). http://geodesic.mathdoc.fr/item/EJDE_2012__2012__a72/