Fractional Hardy-Sobolev equations with nonhomogeneous terms

TL;DR

This paper investigates the existence and multiplicity of positive solutions for fractional Hardy-Sobolev equations with nonhomogeneous terms, employing profile decomposition techniques to handle critical nonlinearities.

Contribution

It introduces new results on the existence of multiple positive solutions for nonlocal fractional equations with critical nonlinearities and external terms.

Findings

Existence of at least two positive solutions

Profile decomposition of Palais-Smale sequences

Handling of critical Hardy-Sobolev nonlinearities

Abstract

The paper deals with existence and multiplicity of positive solutions to nonlocal equations with critical Hrardy-Sobolev nonlinearities and external terms. We establish the profile decomposition of the Palais-Smale sequences associated with the functional and existence of at least two positive solutions to the equation.