Spectrum of periodic Sturm-Liouville problem defined in two disjoint intervals

In this thesis, some spectral properties of the periodic Sturm-Liouville problem defined in two disjoint intervals were investigated. The thesis consists of five parts. In the first part, the fields in which the Sturm-Liouville theory is used are examined. In the second part, the transformation of the physical problems into the Sturm-Liouville problems was investigated. In the third part, the necessary definitions and theorems related to the Sturm-Liouville problems, are given. In the fourth part, initial-value problems related to our problem are examined, some integral equations, asymptotic formulas and characteristic equations are defined. In the last part, the results obtained in this thesis are given.