Eigenvalues and normalized eigenfunctionsof discontinuous Sturm-Liouville problem with transmission conditions

In this study, discontinuous Sturm-Liouville problems which contain eigenvalue parameters both in equation and in the boundary conditions are investigated. We introduce an operator-theoretic interpretation, extend some classic results for regular Sturm-Liouville problems and obtain asymptotic approx...

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Bibliographic Details
Published in:Reports on mathematical physics 2004-08, Vol.54 (1), p.41-56
Main Authors: Mukhtarov, O.Sh, Kadakal, Mahir, Muhtarov, F.Ş.
Format: Article
Language:English
Subjects:
discontinuous boundary-value-problems
eigenfunctions
eigenvalues
Sturm-Liouville problems
transmission conditions
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Summary:In this study, discontinuous Sturm-Liouville problems which contain eigenvalue parameters both in equation and in the boundary conditions are investigated. We introduce an operator-theoretic interpretation, extend some classic results for regular Sturm-Liouville problems and obtain asymptotic approximate formulae for eigenvalues and normalized eigenfunctions. By modifying some techniques of [2, 6, 7] we obtain asymptotic formulae for eigenvalues and normalized eigenfunctions. In the special case, when our problem is continuous, the obtained results coincide with the corresponding results in [2].
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(04)80004-1