Journal of Mathematics of Kyoto University

On discontinuous Sturm-Liouville problems with transmission conditions

O. Sh. Mukhtarov, Mahir Kadakal, and F. S. Muhtarov

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Abstract

We consider a discontinuous Sturm-Liouville equation together with eigenparameter dependent boundary conditions and two supplementary transmission conditions at the point of discontinuity. By modifying some techniques of [2], [11] and [14] we extend and generalize some approach and results of classic regular Sturm-Liouville problems to the similar problems with discontinuities. In particular, we introduce a special Hilbert space formulation such a way that the considered problem can be interpreted as an eigenvalue problem of suitable self-adjoint operator, then we construct the Green function and resolvent operator and derive an asymptotic formulas for eigenvalues and normalized eigenfunctions.

Article information

Source
J. Math. Kyoto Univ., Volume 44, Number 4 (2004), 779-798.

Dates
First available in Project Euclid: 14 August 2009

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1250281698

Digital Object Identifier
doi:10.1215/kjm/1250281698

Mathematical Reviews number (MathSciNet)
MR2118041

Zentralblatt MATH identifier
1098.34069

Subjects
Primary: 34L20: Asymptotic distribution of eigenvalues, asymptotic theory of eigenfunctions
Secondary: 34B24: Sturm-Liouville theory [See also 34Lxx] 34B27: Green functions

Citation

Mukhtarov, O. Sh.; Kadakal, Mahir; Muhtarov, F. S. On discontinuous Sturm-Liouville problems with transmission conditions. J. Math. Kyoto Univ. 44 (2004), no. 4, 779--798. doi:10.1215/kjm/1250281698. https://projecteuclid.org/euclid.kjm/1250281698


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