Expansion theorems for discontinuous Sturm-Liouville problems

Abstract

In this paper, we investigate a discontinuous Sturm-Liouville problem which has several discontinuities inside a finite interval and eigenparameter dependent on one of the boundary conditions. We construct Green’s function and the resolvent operator for this problem and prove theorems about the eigenfunction expansion for Green’s function and the modified Parseval equality in the special Hilbert space.