Existence and multiplicity of solutions for a Dirichlet problem in fractional Orlicz–Sobolev spaces

Abstract

In this paper, we first prove the existence of solutions to Dirichlet problems involving the fractional g-Laplacian operator and lower order terms by appealing to sub- and supersolution methods. Moreover, we also state the existence of extremal solutions. Afterward, and under additional assumptions on the lower order structure, we establish by variational techniques the existence of multiple solutions: one positive, one negative and one with non-constant sign.