{
  "id": "1808.02469",
  "version": "v1",
  "published": "2018-08-07T17:32:26.000Z",
  "updated": "2018-08-07T17:32:26.000Z",
  "title": "Multiplicity of solutions for a nonlocal elliptic PDE involving singularity",
  "authors": [
    "S. Ghosh",
    "D. Choudhuri"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove the existence of multiple solutions for a nonlinear nonlocal elliptic PDE involving a singularity which is given as \\begin{eqnarray} (-\\Delta_p)^s u&=& \\frac{\\lambda}{u^\\gamma}+u^q~\\text{in}~\\Omega,\\nonumber u&=&0~\\text{in}~\\mathbb{R}^N\\setminus\\Omega,\\nonumber u&>& 0~\\text{in}~\\Omega\\nonumber, \\end{eqnarray} where $\\Omega$ is an open bounded domain in $\\mathbb{R}^N$ with smooth boundary, $N>ps$, $s\\in (0,1)$, $\\lambda>0$, $0<\\gamma<1$, $1<p<\\infty$, $p-1<q\\leq p_s^{*}=\\frac{Np}{N-ps}$. We employ variational techniques to show the existence of multiple positive weak solutions of the above problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-07T17:32:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J35",
      "35J60"
    ],
    "keywords": [
      "singularity",
      "multiplicity",
      "nonlinear nonlocal elliptic pde",
      "multiple positive weak solutions",
      "employ variational techniques"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}