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

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, so-called
 transmission conditions. We first prove that eigenvalues real and system eigenfunctions is an orthogonal system. Secondly, some auxiliary initial-value problems transmittal-characteristic function constructed in terms solutions these problems. Finally, we
 establish considered problem zeros function.