Sturm Liouville Problem with Discontinuity Conditions at Several Points

Abstract

In this paper we deal with the computation of the eigenvalues of Sturm Liouville problem with several discontinuity conditions (transmission conditions) inside a finite interval and parameter dependent boundary condition. By using an operator theoretic interpretation we extend some classic results for regular Sturm Liouville problems. A symmetric linear operator A is defined in an appropriate Hilbert space such that the eigenvalues of such a problem coincide with those of A. Also, we obtained asymptotic formulaes for the eigenvalues and corresponding eigenfunctions.