Existence Results for a critical fractional equation

TL;DR

This paper establishes existence results for a critical fractional equation involving the fractional Laplacian and integro-differential operators, using variational methods and mountain-pass techniques.

Contribution

It extends existence results to critical fractional equations with integro-differential operators, including the fractional Laplacian, and accommodates small singular perturbations.

Findings

Existence of solutions for critical fractional equations proven.

Applicability of mountain-pass theorem to integro-differential operators demonstrated.

Results include equations with added small singular terms.

Abstract

We are concerned with existence results for a critical problem of Brezis-Nirenberg Type involving an integro-differential operator. Our study includes the fractional Laplacian. Our approach still applies when adding small singular terms. It hinges on appropriate choices of parameters in the mountain-pass theorem