# Bifurcation results for problems with fractional Trudinger-Moser nonlinearity

## TL;DR

This paper proves the existence of multiple solutions for a fractional Laplacian problem with critical exponential nonlinearity, extending previous results for the N-Laplacian by employing topological methods and a fractional Trudinger-Moser inequality.

## Contribution

It introduces a novel approach combining cohomological linking and a recent fractional Trudinger-Moser inequality to establish bifurcation results for nonlinear problems with exponential growth.

## Key findings

- Multiple solutions established for fractional Laplacian with exponential nonlinearity
- Extension of bifurcation results from N-Laplacian to fractional operators
- Application of topological methods in fractional nonlinear analysis

## Abstract

By using a suitable topological argument based on cohomological linking and by exploiting a Trudinger-Moser inequality in fractional spaces recently obtained, we prove existence of multiple solutions for a problem involving the nonlinear fractional laplacian and a related critical exponential nonlinearity. This extends results in the literature for the N-Laplacian operator.