Existence result for fractional problems with logarithmic and critical exponential nonlinearities

TL;DR

This paper proves the existence of solutions for a fractional elliptic equation with challenging logarithmic and exponential nonlinearities using advanced inequalities and critical point theory.

Contribution

It extends previous work to fractional $N/s$-Laplacian equations with logarithmic nonlinearities, overcoming compactness issues with fractional Trudinger-Moser inequality.

Findings

Existence of nontrivial solutions established.

Extended results to fractional $N/s$-Laplacian equations.

Applied fractional Trudinger-Moser inequality to overcome compactness issues.

Abstract

We study the existence of nontrivial solutions for a nonlinear fractional elliptic equation in presence of logarithmic and critical exponential nonlinearities. This problem extends [5] to fractional $N/s$-Laplacian equations with logarithmic nonlinearity. We overcome the lack of compactness due to the critical exponential nonlinearity by using the fractional Trudinger-Moser inequality. The existence result is established via critical point theory.