Some spectral properties of Sturm-Liouville problem with transmission conditions

Abstract

We investigate the boundary-value problem generated by the Sturm-Liouville equation with discontinuous coefficients, eigenparameter dependent boundary conditions and transmission conditions at the point of discontinuity. With a different approach we introduce an adequate Hilbert space formulation, investigate some properties of eigenvalues, Green's function and resolvent operator, and find simple conditions on the coefficients which guarantee the self-adjointness of the considered problem.