# A Sub-Density Theorem of Sturm-Liouville Eigenvalue Problem with Finitely Many Singularities

## TL;DR

This paper analyzes the eigenvalue distribution of Sturm-Liouville problems with finitely many singularities, revealing an asymptotically periodic structure and explicitly describing the potential's singularities in eigenvalue asymptotics.

## Contribution

It establishes a sub-density theorem for eigenvalues with singular potentials, linking eigenvalue distribution to the potential's singularities using entire function theory.

## Key findings

- Eigenvalues exhibit asymptotically periodic distribution.
- Explicit description of potential singularities in eigenvalue asymptotics.
- Theoretical connection between eigenvalue distribution and potential singularities.

## Abstract

We study the distribution of the Sturm-Liouville eigenvalues of a potential with finitely many singularities. There is an asymptotically periodical structure on this class of eigenvalues as described by the entire function theory. We describe the singularities of its potential function explicitly in its eigenvalue asymptotics.