Eigenvalue problems for Sturm Liouville equations with transmission conditions

In this study, we consider a Sturm Liouville type boundary-value problem with eigenparameter-dependent boundary conditions and with two supplementary transmission conditions at one inner point of a finite interval under consideration. We modify some techniques of classical Sturm Liouville theory and suggest a new approach for the investigation of eigenvalues and eigenfunctions of this type of boundary-value problem.