Infinitely many sign-changing solutions for a class of elliptic problem with exponential critical growth

TL;DR

This paper proves the existence of infinitely many nonradial solutions to a two-dimensional elliptic boundary value problem with nonlinearities exhibiting exponential critical growth, expanding understanding of solution multiplicity in such contexts.

Contribution

It establishes the existence of infinitely many sign-changing solutions for a class of elliptic problems with exponential critical growth, a novel result in this setting.

Findings

Infinitely many nonradial solutions exist.

Solutions change sign.

Results apply to problems with exponential critical growth.

Abstract

In this work we prove the existence of infinitely many nonradial solutions that change signal to the problem $-\Delta u=f(u)$ in $B$ with $u=0$ on $\partial B$, where $B$ is the unit ball in $\mathbb{R}^2$ and $f$ is a continuous and odd function with exponential critical growth.