Investigation of eigenfunctions of a boundary value problem with nonlocal boundary conditions

In this paper, we consider the solution of a spectral boundary value problem with non-local boundary conditions of a special kind. The authors propose numerical methods for finding eigenvalues and corresponding eigenfunctions. The dependence of eigenvalues and eigenfunctions on a real parameter is investigated. The presented results demonstrate the applicability of the given boundary conditions to solve the problem of maximizing the difference between the first two eigenvalues and can be proposed, which can be used in the study of the phenomena of superfluidity and superconductivity, numerical methods, in the study of difference circuits, as well as the electromagnetic diffraction problem on conductive thin screens.