Green function of one discontinuous sturm-liouville problem

In this study, we consider one discontinuous Sturm-liouville problem with two supplementary transmission at the one inner point of discontinuity and seek some spectral properties of this problem when the potential of the differantial equation may have discontinuity at the one iner point and the eigenparameter appears in the differential equation. We give an operator-theoretic interpretation and obtain asymptotic formulas for eigenvalues and corresponding eigenfunctions. Finally, we construct Green's function and obtain the asymptotic representation of Green's function.