Higher nonlocal problems with bounded potential

TL;DR

This paper investigates a class of nonlocal fractional Laplacian equations with two parameters, establishing the existence of three weak solutions using critical point theory in fractional Sobolev spaces.

Contribution

It introduces new existence results for nonlocal fractional problems with non-affine parameter dependence, expanding the analytical framework for such equations.

Findings

Existence of three weak solutions for the class of problems studied

Application of an abstract critical point theorem in fractional Sobolev spaces

Handling non-affine parameter dependence in nonlocal equations

Abstract

The aim of this paper is to study a class of nonlocal fractional Laplacian equations depending on two real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci, we establish the existence of three weak solutions for nonlocal fractional problems exploiting an abstract critical point result for smooth functionals. We emphasize that the dependence of the underlying equation from one of the real parameter is not necessarily of affine type.