Study the properties of spectral characteristics and eigenfunctions for Sturm-Liouville boundary value problems

In this study, we provide an overview of the Sturm-Liouville operator’s spectral theory on a finite interval. Also, we study the main spectral characteristics for the second-order differential operator, and we show that the eigenvalues and eigenfunctions are real and the characteristic functions are simple. The Sturm-Liouville eigenvalues of that problem are non-degenerate; for every eigenvalue, there exists only one linearly independent solution.