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

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arxiv 1909.06584 v1 pith:VX2WYONI submitted 2019-09-14 math.AP

Sabri Bahrouni , Hichem Ounaies This is my paper · ORCID
classification math.AP
keywords fractionalorlicz-sobolevembeddingnon-localtheoremstriangleapplicationsclass
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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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Cited by 2 Pith papers

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  1. Comparison principle for Singular Fractional $ g- $Laplacian Problems

    math.AP 2025-07 conditional novelty 6.0 of 10

    A comparison principle and uniqueness theorem for singular fractional g-Laplacian problems with combined singular and power nonlinearities.

  2. Holder continuity of an alternating Erdos series on prime K-tuples

    math.GM 2025-04 reject novelty 3.0 of 10

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