Nonlocal critical elliptic equations in homogeneous fractional Sobolev spaces

TL;DR

This paper establishes multiple solutions for nonlocal critical elliptic equations in fractional Sobolev spaces using advanced topological and regularity techniques.

Contribution

It introduces new multiplicity results for nonlocal critical elliptic equations leveraging an abstract critical point theorem and novel regularity findings.

Findings

Proved existence of multiple solutions for nonlocal elliptic equations

Developed a new regularity result for fractional p-Laplacian equations

Established compact embeddings in fractional Sobolev spaces

Abstract

We prove new multiplicity results for some nonlocal critical growth elliptic equations in homogeneous fractional Sobolev spaces. The proofs are based on an abstract critical point theorem based on the ${\mathbb Z}_2$-cohomological index and on a novel regularity result for fractional $p$-Laplacian equations as well as on some compact embeddings.