ABSTRACT
This chapter has a traditional introductory character. Various approaches to the investigation and approximate solution of eigenvalue problems are demonstrated in the case of the classical SturmLiouville problem with boundary conditions of the first, the second, or the third kind, and also periodic boundary conditions (the fourth kind). One of the main approaches to these eigenvalue problems is based on the analysis of solutions of the corresponding differential equation. The other approaches discussed here are those based on the direct variational method and the methods of functional analysis widely used in theoretical investigations and numerical procedures.
