Prüfer analysis of periodic Sturm-Liouville problem with transmission condition

There are several studies in the literature that prefer the Prüfer transformation to show the existence of the eigenvalues of the Sturm-Liouville problem. Within the scope of this thesis, we first focused on these studies in the literature, and then discussed a periodic Sturm-Liouville problem with transmission condition. We chose this problem because the spectral analysis of a Sturm-Liouville problem with transmission condition has not been handled using the Prüfer transformation before. The transmission condition mentioned here is given at an inner discontinuity point of the interval where the problem we have chosen is defined. As a result of the investigations we have made, we have reached our goal and demonstrated the existence of the eigenvalues of a periodic Sturm-Liouville problem with transmission condition by Prüfer transformation. Thus, it has been revealed that this analysis method we have considered is simpler and requires less background than other methods in the literature for the same problem.