{
  "id": "1804.05590",
  "version": "v1",
  "published": "2018-04-16T10:14:07.000Z",
  "updated": "2018-04-16T10:14:07.000Z",
  "title": "Multiplicity of solutions to an elliptic problem with singularity and measure data",
  "authors": [
    "S. Ghosh",
    "A. Panda",
    "D. Choudhuri"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove the existence of multiple nontrivial solutions of the following equation. \\begin{align*} \\begin{split} -\\Delta_{p}u & = \\frac{\\lambda}{u^{\\gamma}}+g(u)+\\mu\\,\\,\\mbox{in}\\,\\,\\Omega, u & = 0\\,\\, \\mbox{on}\\,\\, \\partial\\Omega, u&>0 \\,\\,\\mbox{in}\\,\\,\\Omega, \\end{split} \\end{align*} where $\\Omega \\subset \\mathbb{R}^N$ is a smooth bounded domain with $N \\geq 3$, $1 < p-1 < q$ , $ \\lambda>0$, $g$ satisfies certain conditions, $\\mu\\geq 0$ is a Radon measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-16T10:14:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic problem",
      "measure data",
      "multiplicity",
      "singularity",
      "multiple nontrivial solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}