Ground states of nonlocal scalar field equations with Trudinger-Moser critical nonlinearity

TL;DR

This paper studies the existence of ground state solutions for nonlocal scalar field equations with fractional Laplacian and Trudinger-Moser critical growth, addressing compactness issues on the real line.

Contribution

It establishes the existence of ground states for a class of nonlocal equations with critical exponential nonlinearities, overcoming compactness challenges.

Findings

Proved existence of ground state solutions.

Addressed lack of compactness in unbounded domains.

Handled Trudinger-Moser critical growth nonlinearities.

Abstract

We investigate the existence of ground state solutions for a class of nonlinear scalar field equations defined on whole real line, involving a fractional Laplacian and nonlinearities with Trudinger-Moser critical growth. We handle the lack of compactness of the associated energy functional due to the unboundedness of the domain and the presence of a limiting case embedding.