Solutions of Sturm-Liouville problems with green functions

In this study, solutions of Sturm-Liouville problems with Green function are discussed. In the first chapter, the emergence and development process of the problem is summarized with a historical perspective. In the second chapter, basic definitions and theorems, boundary conditions, introduction of Green function and its properties, physical meaning and its expansion as an eigenfunction series are examined. In the third chapter, Green functions for Sturm-Liouville boundary value problems, transformation of some important differential equations into Sturm - Liouville form, asymptotic behaviors of Sturm-Liouville problems, and Green function for tree graphics are included. In the fourth chapter, applications of Sturm-Liouville problems in many fields such as physics, mechanics and quantum are included.