Infinitely many solutions for semilinear nonlocal elliptic equations under noncompact settings

TL;DR

This paper establishes the existence of infinitely many solutions for a class of semilinear nonlocal elliptic equations, specifically fractional Brezis-Nirenberg problems, in noncompact settings where traditional Sobolev embeddings do not hold.

Contribution

It proves the existence of infinitely many solutions for fractional Brezis-Nirenberg problems in noncompact domains, extending previous results to nonlocal equations without compact Sobolev embeddings.

Findings

Infinitely many solutions exist for the fractional Brezis-Nirenberg problem.

Solutions are established in noncompact domain settings.

The work extends classical results to nonlocal, noncompact scenarios.

Abstract

In this paper, we study a class of semilinear nonlocal elliptic equations posed on settings without compact Sobolev embedding. More precisely, we prove the existence of infinitely many solutions to the fractional Brezis-Nirenberg problems on bounded domain.