Spectral theory of sturm-liouville problem for difference equations

This study consists of four chapters. In the first chapter, the appearance, development, history and application fields of difference equations are given. In the second chapter, fundamental definitions and theorems, solution methods for difference equations and relation between differential equations and difference equations are given. In the third chapter, boundary value problem, disconjugacy concept, Green function, generalized and simple zeros are given and the uniqueness of solution is analyzed. In the last chapter of this thesis, Sturm-Liouville problem, its eigenvalues and eigenfunctions are analyzed. Furthermore, the map of solution is obtained for Sturm-Liouville problem by means of variation of parameters method. Key Words: Difference Equations, Sturm-Liouville, Eigenvalue, Eigenfunction, Casoratyan