Spectral properties of a periodic sturm-liouville problemwith transition conditions

In this thesis, some spectral properties of a periodic boundary-value-transition problem were investigated. This study consists of five chapters. The first chapter provides brief information on the Sturm-Liouville problem and its applications in natural science. In the second chapter, information about the studies in the literature on Sturm-Liouville theory is given. In the third chapter, general definitions and theorems related to Sturm-Liouville problems are given, which will form the basis of the thesis work. In the fourth chapter, it has been shown that the eigenvalues of the periodic Sturm-Liouville boundary-value-transition problem are real, the eigenfunctions corresponding to different eigenvalues are orthogonal. A comparison theorem, Sturm-Picone theorem and some other theorems are also given. The last chapter is devoted to the results obtained in this work.