# Perturbation results involving the 1-Laplace operator

## TL;DR

This paper investigates how solutions to eigenvalue problems involving the 1-Laplace operator behave under perturbations, demonstrating convergence of eigenvalues and solutions using nonsmooth critical point theory.

## Contribution

It introduces a new analysis of perturbed 1-Laplace eigenvalue problems and proves convergence results using nonsmooth critical point theory.

## Key findings

- Eigenvalues of perturbed problems converge to unperturbed eigenvalues
- Existence of solution sequences for perturbed eigenvalue problems
- Application of nonsmooth critical point theory based on weak slope

## Abstract

We consider perturbed eigenvalue problems of the 1-Laplace operator and verify the existence of a sequence of solutions. It is shown that the eigenvalues of the perturbed problem converge to the corresponding eigenvalue of the unperturbed problem as the perturbation becomes small. The results rely on nonsmooth critical point theory based on the weak slope.