Nonlocal problems with critical Hardy nonlinearity

TL;DR

This paper uses variational methods to prove the existence and multiplicity of solutions for nonlocal fractional p-Laplacian problems involving Hardy and Sobolev nonlinearities at various growth levels.

Contribution

It introduces new results on solution existence and multiplicity for nonlocal problems with combined Hardy and Sobolev nonlinearities at critical and subcritical growth.

Findings

Existence of solutions established for subcritical growth.

Multiplicity results for solutions demonstrated.

Solutions also exist at critical growth levels.

Abstract

By means of variational methods we establish existence and multiplicity of solutions for a class of nonlinear nonlocal problems involving the fractional p-Laplacian and a combined Sobolev and Hardy nonlinearity at subcritical and critical growth.