Spectrum of periodic Sturm-Liouville problems involving additional transmission conditions

Abstract

This paper presents some spectral properties of the Sturm-Liouville equation associated with periodic boundary conditions and additional transmission conditions at one interior singular point. We derived asymptotic formulas for the eigenvalues of the considered problem. Note that the problem under consideration has not been investigated previously. To illustrate the originality of the results we constructed a simple example of a periodic Sturm-Liouville problem with transmission conditions, whose eigenvalues may not be simple.