Orthogonality of sturm-liouville problems and some asymptotic behaviours

In this thesis, we discussed some important aspects of Sturm-Liouville theory such as orthogonality, Fourier series and asymptotic formulas for eigenvalues and eigenfunctions. After giving an introduction about the history of Sturm-Liouville Theory. We gave the way to convert any problem into regular Sturm-Liouville problem by finding suitable weight function. We included a method of finding asymptotic formulas for eigenvalues and eigenfunctions of Sturm-Liouville Problems. We also obtain an important formula about the solutions of a specific SL-problem and obtain formulas of eigenvalues and eigenfunctions of this problem.