Problem for the Sturm–Liouville equation with the square of the spectral parameter in the boundary condition of the third kind

Recieved: 01/09/2026

Accepted: 02/17/2026

Keywords: spectral problem, Sturm-Liouville equation

Available in the on-line version with: 24.07.2026

To cite this article

Kapustin N.Yu., Mammetsahedova S., Kholomeeva A.A. Problem for the Sturm–Liouville equation with the square of the spectral parameter in the boundary condition of the third kind. // Moscow University Journal. Series 15. Computational Mathematics and Cybernetics. 2026. N 2, p.36-42 https://doi.org/10.55959/MSU/0137–0782–15–2026–50–2–36–42.

This work is licensed under a Сreative Commons Atribiution - NonCommercial 4.0 International (CC BY-NC 4.0)

Kapustin N.Yu. (Lomonosov Moscow State University (MSU))
Mammetsahedova S. (Lomonosov Moscow State University (MSU))
Kholomeeva A.A. (Lomonosov Moscow State University (MSU))

Abstract

In this paper, we study the spectral problem for the Sturm-Liouville equation. One of the boundary conditions is a homogeneous Dirichlet condition, and the other is a condition of the third kind, and contains the square of the spectral parameter. A biorthogonal system to the system of eigenfunctions of the task is constructed. The problems of the basis property and the Riesz basis property of system of eigenfunctions are investigated.