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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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

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

First available in Project Euclid: 14 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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