Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems

Abstract

In the present paper, we deal with a new continuous and compact embedding theorems for the fractional Orlicz-Sobolev spaces, also, we study the existence of infinitely many nontrivial solutions for a class of non-local fractional Orlicz-Sobolev Schrödinger equations whose simplest prototype is $$(-△{)}_m^{s}u+V(x)m(u)=f(x,u),x\in {\mathbb{R}}^d,$$ where $0<s<1$, $d\ge 2$ and $(-△{)}_m^s$ is the fractional $M$-Laplace operator. The proof is based on the variant Fountain theorem established by Zou.

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