Multiplicity of Solutions for Nonlocal Fractional Equations with Nonsmooth Potentials

This paper is concerned a specific category of nonlocal fractional Laplacian problems that involve nonsmooth potentials. By utilizing an abstract critical point theorem for nonsmooth functionals and combining it with the analytical framework on fractional Sobolev spaces developed by Servadei and Valdinoci, we are able to establish the existence of at least three weak solutions for nonlocal fractional problems. Moreover, this work also generalizes and improves upon certain results presented in the existing literature.