# Oscillation properties of one boundary problem of fourth order with a spectral parameter in the boundary conditions

## TL;DR

This paper investigates a fourth-order boundary value problem with a spectral parameter in the boundary condition, establishing the simplicity of its spectrum and analyzing the oscillation behavior of its eigenfunctions.

## Contribution

It proves the spectrum's simplicity and explores oscillation properties of eigenfunctions for a specific fourth-order boundary problem with spectral parameters.

## Key findings

- Spectrum is simple.
- Eigenfunctions exhibit specific oscillation properties.
- Results contribute to understanding spectral problems with boundary parameters.

## Abstract

For one boundary problem of fourth order with a spectral parameter in the boundary condition we prove the simplicity of the spectrum and the oscillation properties of the system of the eigenfunctions derivatives.