Asymptotic formulas for eigenvalues of Sturm-Liouville operator

This thesis consists of seven chapters. In the first chapter the history of spectral theory of Sturm-Liouville operator were given. In the second chapter some fundemental definitions, often used is spectral theory of differential operators, were given. In the third general informations for Sturm-Liouville operator , regular and singular Sturm-Liouville problem, asymptotic formula for eigenvalues with Dirichlet boundary condition were investigated. In the fourth chapter asymptotic formula for eigenvalues of singular Sturm-Liouville problem and spectral theory of this problem is investigated. In the fifth chapter solution functions of Sturm-Liouville operator with Coulomb potential under dirichlet boundary conditions are obtained and asymptotic formula for eigenvalues are found. In the six chapter solution functions of Diffusion operator under dirichlet boundary conditions are obtained and Counting lemma for this operator is proved and asymptotic formula for eigenvalues is found. In the seven chapter solution functions of Hydrogen atom equation under dirichlet boundary conditions are obtained and asymptotic behavior of eigenvalues is examined.