# On a differential operator with absent spectrum

## TL;DR

This paper investigates a higher-order differential operator with special boundary conditions, providing an example where the spectral problem has no eigenvalues, challenging traditional spectral theory assumptions.

## Contribution

It constructs a novel example of a differential operator with degenerate boundary conditions that lacks eigenvalues, expanding understanding of spectral properties.

## Key findings

- Constructed a differential operator with no eigenvalues
- Demonstrated the impact of degenerate boundary conditions on spectrum
- Challenged existing spectral theory assumptions

## Abstract

In this paper, we consider spectral problem for the nth order ordinary differential operator with degenerate boundary conditions. We construct a nontrivial example of boundary value problem which has no eigenvalues.