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Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems (1909.06584v1)
Published 14 Sep 2019 in math.AP
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 Schr\"{o}dinger equations whose simplest prototype is $$(-\triangle){s}_{m}u+V(x)m(u)=f(x,u),\ x\in\mathbb{R}{d},$$ where $0<s<1$, $d\geq2$ and $(-\triangle){s}_{m}$ is the fractional $M$-Laplace operator. The proof is based on the variant Fountain theorem established by Zou.