Jessica Ramström: Sturm-Liouville theory

Abstract: This thesis presents the fundamentals of Sturm–Liouville theory, which provides a framework for a class of second-order differential equations. Properties of the solutions of these equations, known as eigenfunctions, are discussed and proved. In particular, the orthogonality of eigenfunctions and Sturm’s comparison theorem are established. Furthermore, a method for solving Sturm-Liouville problems is described and illustrated with a concrete example. Finally, the influence of boundary conditions on the eigenvalues and the associated eigenfunctions is examined.