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arXiv · 1909.06584

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

Sabri Bahrouni·Hichem Ounaies
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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.

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Sabri Bahrouni, Hichem Ounaies. 2019-09-14. Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems. https://arxiv.org/abs/1909.06584

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