Variational approach to a symmetric boundary value problem generated by a system of equations and separated boundary conditions

Abstract

This work provides some information on the eigenvalues and eigenfunctions of a problem which is constructed by a system of equations and symmetric boundary conditions that includes the ordinary second‐order Sturm–Liouville boundary value problem. In particular, we show that the problem has an infinite number of discrete eigenvalues with a greatest lower bound and the corresponding eigenfunctions are complete in mean and energy. We introduce the results using the variational approach that enables us to consider only continuous pair functions instead of absolutely continuous pair functions.