Volkan Ala and Khanlar R. Mamedov.  On a Discontinuous Sturm-Liouville Problem with Eigenvalue Parameter in the Boundary Conditions.  Dynamic Systems and Applications 29 (2020) No. 1, 182-191

https://doi.org/10.46719/dsa202029.1.11

ABSTRACT.
In this study, we consider one class discontinuous Sturm-Liouville equation with
eigenparameter-dependent boundary and transmission conditions. In mathematical physics, when the string has different densities and loaded additionally with point masses, we encounter with such problems as spectral problem during the solution of suitable dynamic equations. The aim of this paper is to investigate the completeness, minimality and basis properties of the considered boundary value problem.

AMS (MOS) Subject Classification. 34L10, 34B24, 47E05.
Key Words and Phrases. Eigenvalues, Completeness, Riesz Basis.