The Transmittal-Characteristic Function of Three-Interval Periodic Sturm-Liouville Problem with Transmission Conditions

Authors : Kadriye AYDEMİR, Oktay MUKHTAROV

Pages : 26-34

Doi:10.53570/jnt.1018600

View : 15 | Download : 9

Publication Date : 2021-12-31

Article Type : Research Paper

Abstract :In this paper, we study the periodic Sturm-Liouville problem, defined on three non-intersecting intervals with four supplementary conditions which are imposed at two internal points of interaction, the so-called transmission conditions. We first prove that the eigenvalues are real and the system of eigenfunctions is an orthogonal system. Secondly, some auxiliary initial-value problems are defined and transmittal-characteristic function is constructed in terms of solutions of these initial-value problems. Finally, we establish that the eigenvalues of the considered problem are the zeros of the transmittal-characteristic function.
Keywords : Periodic transmittal Sturm Liouville problem, characteristic function, spectrum