Finite difference sturm-liouville problem

This thesis consists of three chapters. In the first chapter, some concepts which are used in this thesis are given and some fundamental properties of Sturm-Liouville operator are examined. In the second chapter, difference equation and Sturm-Liouville difference operator is studied briefly. We obtained asymptotic formulas for above discrete and contionuous Liouville normal form eigenvalue problem with general boundary condition. In the third chapter, by using finite difference method, asymptotics forms and uniqueness theorem are given for the problem which is given in section 2.