Eigenvalues and eigenfunctions of discontinuous Sturm-Liouville problems with eigenparameter-dependent boundary conditions (Q1882130)

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 \textit{F. S. Mukhtarov, M. Kadakal} and \textit{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.