{
  "id": "1812.01838",
  "version": "v1",
  "published": "2018-12-05T07:20:45.000Z",
  "updated": "2018-12-05T07:20:45.000Z",
  "title": "Existence of infinitely many solutions for a nonlocal elliptic PDE involving singularity",
  "authors": [
    "S. Ghosh",
    "D. Choudhuri"
  ],
  "comment": "17 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we will prove the existence of infinitely many positive weak solutions to the following nonlocal elliptic PDE. \\begin{align} (-\\Delta)^s u&= \\frac{\\lambda}{u^{\\gamma}}+ f(x,u)~\\text{in}~\\Omega,\\nonumber u&=0~\\text{in}~\\mathbb{R}^N\\setminus\\Omega,\\nonumber \\end{align} where $\\Omega$ is an open bounded domain in $\\mathbb{R}^N$ with Lipschitz boundary, $N>2s$, $s\\in (0,1)$. We will employ variational techniques to show the existence of infinitely many weak solutions of the above problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-12-05T07:20:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J35",
      "35J60",
      "35J75"
    ],
    "keywords": [
      "nonlocal elliptic pde",
      "singularity",
      "employ variational techniques",
      "open bounded domain",
      "lipschitz boundary"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}