Spectral Properties of Discontinuous Sturm–Liouville Problems with a Finite Number of Transmission Conditions

In this paper we investigate discontinuous two-point boundary value problems with eigenparameter in the boundary conditions and with transmission conditions at the finitely many points of discontinuity. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalu...

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Bibliographic Details
Published in:Mediterranean journal of mathematics Vol. 13; no. 1; pp. 153 - 170
Main Authors: Şen, Erdoğan, Mukhtarov, O. Sh
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.02.2016
Subjects:
Mathematics
Mathematics and Statistics
34B27
47E05
transmission conditions
spectrum
completeness
eigenparameter-dependent boundary conditions
asymptotics of eigenvalues and eigenfunctions
34L10
34L20
Sturm–Liouville problems
ISSN:1660-5446, 1660-5454
Online Access:Get full text
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Summary:In this paper we investigate discontinuous two-point boundary value problems with eigenparameter in the boundary conditions and with transmission conditions at the finitely many points of discontinuity. A self-adjoint linear operator A is defined in a suitable Hilbert space H such that the eigenvalues of the considered problem coincide with those of A . We obtain asymptotic formulas for the eigenvalues and eigenfunctions. Also we show that the eigenelements of A are complete in H .
ISSN:1660-5446
1660-5454
DOI:10.1007/s00009-014-0487-x