# The infinity-Fucik spectrum

## TL;DR

This paper investigates the asymptotic behavior of the Fucik spectrum for the p-Laplace operator as p approaches infinity, characterizing the limit spectrum and providing explicit computations for specific domains.

## Contribution

It offers a detailed analysis of the limit spectrum of the p-Laplace operator's Fucik spectrum as p tends to infinity, including explicit examples.

## Key findings

- Characterization of the limit equation as p approaches infinity
- Description of the limit spectrum structure
- Explicit spectrum computations for specific domain configurations

## Abstract

In this article we study the behavior as $p \nearrow+\infty$ of the Fucik spectrum for $p$-Laplace operator with zero Dirichlet boundary conditions in a bounded domain $\Omega\subset \mathbb{R}^n$. We characterize the limit equation, and we provide a description of the limit spectrum. Furthermore, we show some explicit computations of the spectrum for certain configurations of the domain.