# Asymptotic expansion for the eigenvalues of a perturbed anharmonic oscillator

## TL;DR

This paper derives asymptotic expansions for eigenvalues of a perturbed anharmonic oscillator with piecewise H"older continuous perturbations, analyzing how the H"older constant influences spectral properties.

## Contribution

It provides the first terms of the asymptotic expansion for eigenvalues considering H"older continuous perturbations, a novel analysis in spectral theory.

## Key findings

- Eigenvalues have asymptotic expansions influenced by the H"older constant
- Derived explicit first terms in the eigenvalue asymptotics
- Enhanced understanding of spectral effects of piecewise H"older perturbations

## Abstract

In this article, we study the spectral properties of the perturbation of the generalized anharmonic oscillator. We consider a piecewise H\"older continuous perturbation and investigate how the H\"older constant can affect the eigenvalues. More precisely, we derive several first terms in the asymptotic expansion for the eigenvalues.