Asymptotie of solution functions of a Sturm-Liouville-type problem and the green function

In this study we have examined Sturm-Liouville Problem which has eigenvalue parameter in the boundary conditions.This study has arranged in 5 chapters, in ?The Introduction? chapter, informations related to Sturm-Liouville equation, mathematical physics, Sturm and Liouville has been given.In ?The Literatur? chapter, we have mentioned the general history of boundary value problems for linear differential equations which has eigenvalue parameter and a brief summary of the results obtained from other studies.In ?The General Knowledge? chapter, we have mentioned the general knowledge and definitions about the subject of our thesis.In ?Finding and Discussion? chapter, we have examined eigenvalue of Sturm-Liouville Problem and obtained asymptotic formulas and Green?s function.In ?Conclusions and Recommendations? chapter, we have mentioned possible solutions obtained from the study and important of these solutions.Key Words: Boundary value problem, Sturm-Liouville Theory, Differential operator, eigenvalue, eigenfunction, asymptotic behavior, Green?s Function.