Nonlocal problems at critical growth in contractible domains

TL;DR

This paper establishes the existence of positive solutions for nonlocal fractional Laplacian problems with critical growth nonlinearities in contractible domains, advancing understanding of such equations in specific geometric settings.

Contribution

It provides the first existence proof for positive solutions in contractible domains for fractional Laplacian problems with critical nonlinearities.

Findings

Existence of positive solutions proven

Applicable to fractional Laplacian with critical growth

Results extend previous work to contractible domains

Abstract

We prove the existence of a positive solution for nonlocal problems involving the fractional Laplacian and a critical growth power nonlinearity when the equation is set in a suitable contractible domain.