{
  "id": "2205.05919",
  "version": "v1",
  "published": "2022-05-12T07:13:57.000Z",
  "updated": "2022-05-12T07:13:57.000Z",
  "title": "Problems involving the fractional $g$-Laplacian with Lack of Compactness",
  "authors": [
    "Sabri Bahrouni",
    "Hichem Ounaies",
    "Olfa Elfalah"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove compact embedding of a subspace of the fractional Orlicz-Sobolev space $W^{s, G}\\left(\\mathbb{R}^{N}\\right)$ consisting of radial functions, our target embedding spaces are of Orlicz type. Also, we prove a Lions and Lieb type results for $W^{s,G}\\left(\\mathbb{R}^{N}\\right)$ that works together in a particular way to get a sequence whose the weak limit is nontrivial. As an application, we study the existence of solutions to Quasilinear elliptic problems in the whole space $\\mathbb{R}^N$ involving the fractional $g-$Laplacian operator, where the conjugated function $\\widetilde{G}$ of $G$ doesn't satisfy the $\\Delta_2$-condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-05-12T07:13:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "compactness",
      "quasilinear elliptic problems",
      "lieb type results",
      "fractional orlicz-sobolev space",
      "radial functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}