Some properties of a periodic Sturm-Liouville problem with discontinuity at two points

In this thesis, the periodic Sturm-Liouville boundary-value-transition problem with discontinuity at two points is investigated. The study consists of five chapters. In the first chapter, general information about Sturm-Liouville problems is given. In the second chapter, the works on Sturm-Liouville theory in the literature are mentioned. In the third chapter, some the methods definitions, theorems and proofs of the Sturm-Liouville theory which are used in this thesis are given. In the fourth section, it is shown that the eigenvalues of the periodic Sturm-Liouville boundary-value-transmittion problem are real. Fundamental solutions closely related to the problem are defined. The integral equations corresponding to the fundamental solutions are defined and asymptotic formulas for the fundamental solutions are found by using these integral equations. The characteristic equation corresponding to the problem is determined. It is shown that the eigenvalues of the studied problem coincide with the zeros of the characteristic equation. In the last chapter, the importance of the thesis topic is discussed.