Applications of prüfer transformations in the theory of ordinary differential equations

The solutions of the self-adjoint second order differential equation have been studied by means of classical theorems of the theory of ordinary differential equations. In this thesis, we wish to examine the same theorems using Prüfer transformations techniques which are a generalization of the Poincare phase plane analysis. We begin by proving the Sturm Comparison theorem and the Disconjugacy theorem. Then, to get the necessary and sufficient conditions for boundedness of the solutions, we study the asymptotic behaviour of the solution of the equation above , as t infinite. In addition, we use Prüfer transformations to analyse the spectrum of a certain type of Sturm-Liouville eigenvalue problems with some given boundary conditions