Three solutions for a fractional elliptic problems with critical and supercritical growth

TL;DR

This paper investigates the existence and multiplicity of solutions for fractional elliptic problems with critical and supercritical growth using variational methods, truncation, and Moser iteration.

Contribution

It introduces a novel approach combining truncation and Moser iteration to establish at least three solutions for these complex problems.

Findings

Proved existence of at least three solutions.

Applied variational methods to fractional elliptic problems.

Utilized truncation and Moser iteration techniques.

Abstract

In this paper, we deal with the existence and multiplicity of solutions for the fractional elliptic problems involving critical and supercritical Sobolev exponent via variational arguments. By means of the truncation combining with the Moser iteration, we prove that the problems has at least three solutions.