A concave-convex elliptic problem involving the fractional Laplacian

TL;DR

This paper investigates a nonlinear elliptic problem with fractional Laplacian and concave-convex terms, characterizing parameter ranges for solutions and establishing multiple solution results.

Contribution

It provides a complete characterization of parameter ranges for solution existence and proves multiplicity results for a fractional elliptic problem.

Findings

Identified parameter ranges for solution existence.

Proved the existence of multiple solutions.

Characterized the solution set completely.

Abstract

We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize completely the range of parameters for which solutions of the problem exist and prove a multiplicity result.