{
  "id": "1804.03812",
  "version": "v1",
  "published": "2018-04-11T04:57:59.000Z",
  "updated": "2018-04-11T04:57:59.000Z",
  "title": "Existence of multiple solutions to an elliptic problem with measure data",
  "authors": [
    "Amita Soni",
    "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 & = \\lambda |u|^{q-2}u+f(x,u)+\\mu\\,\\,\\mbox{in}\\,\\,\\Omega, u & = 0\\,\\, \\mbox{on}\\,\\, \\partial\\Omega; \\end{split} \\end{align*} where $\\Omega \\subset \\mathbb{R}^N$ is a smooth bounded domain with $N \\geq 3$, $1 < q^{\\prime} < q < p-1; \\; \\lambda,\\;$ and $f$ satisfies certain conditions, $\\mu>0$ is a Radon measure, $q^{\\prime}=\\frac{q}{q-1}$ is the conjugate of $q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-11T04:57:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35J60"
    ],
    "keywords": [
      "multiple solutions",
      "elliptic problem",
      "measure data",
      "multiple nontrivial solutions",
      "smooth bounded domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}