{
  "id": "1804.10699",
  "version": "v1",
  "published": "2018-04-27T22:01:55.000Z",
  "updated": "2018-04-27T22:01:55.000Z",
  "title": "Three solutions for a nonlocal problem with critical growth",
  "authors": [
    "Natalí Ailín Cantizano",
    "Analía Silva"
  ],
  "comment": "10 pages. arXiv admin note: text overlap with arXiv:0808.3143, arXiv:0912.3465",
  "categories": [
    "math.AP"
  ],
  "abstract": "The main goal of this work is to prove the existence of three different solutions (one positive, one negative and one with nonconstant sign) for the equation $(-\\Delta_p)^s u= |u|^{p^{*}_s -2} u +\\lambda f(x,u)$ in a bounded domain with Dirichlet condition, where $(-\\Delta_p)^s$ is the well known $p$-fractional Laplacian and $p^*_s=\\frac{np}{n-sp}$ is the critical Sobolev exponent for the non local case. The proof is based in the extension of the Concentration Compactness Principle for the $p$-fractional Laplacian and Ekeland's variational Principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-27T22:01:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35R01",
      "35R11"
    ],
    "keywords": [
      "nonlocal problem",
      "critical growth",
      "fractional laplacian",
      "ekelands variational principle",
      "concentration compactness principle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}