{
  "id": "1909.06584",
  "version": "v1",
  "published": "2019-09-14T11:55:12.000Z",
  "updated": "2019-09-14T11:55:12.000Z",
  "title": "Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems",
  "authors": [
    "Sabri Bahrouni",
    "Hichem Ounaies"
  ],
  "comment": "No comments",
  "categories": [
    "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-14T11:55:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional orlicz-sobolev space",
      "non-local problems",
      "applications",
      "variant fountain theorem",
      "non-local fractional orlicz-sobolev"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}