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Eigenvalues and eigenfunctions of discontinuous Sturm-Liouville problems with eigenparameter-dependent boundary conditions. (English) Zbl 1052.34030

The asymptotics for the eigenvalues and normalized eigenfunctions of a Sturm-Liouville problem with discontinuous weight are obtained. The boundary conditions depend on the spectral parameters and transmission conditions are satisfied at the point of discontinuity.

We should remark that a quite similar problem has been treated and similar results have been obtained in the paper of F. S. Mukhtarov, M. Kadakal and O. S. Mukhtarov [Int. J. Appl. Math. 12, No. 3, 235–250 (2003; Zbl 1047.34099)]. The methods used in the two papers are slightly different.

MSC:
 34B24 Sturm-Liouville theory 34L20 Asymptotic distribution of eigenvalues for OD operators 47A75 Eigenvalue problems (linear operators) 47E05 Ordinary differential operators