A-priori bounds and multiplicity of solutions for nonlinear elliptic problems involving the fractional [formula omitted]-Laplacian

Abstract

We obtain fundamental imbeddings for fractional Sobolev spaces with variable exponents, which are a generalization of the well-known fractional Sobolev spaces. As an application, we obtain a-priori bounds and multiplicity of solutions to some nonlinear elliptic problems involving the fractional p(⋅)-Laplacian.