{
  "id": "1902.01174",
  "version": "v1",
  "published": "2019-02-04T13:31:06.000Z",
  "updated": "2019-02-04T13:31:06.000Z",
  "title": "Existence of solution for a system involving fractional Laplacians and a Radon measure",
  "authors": [
    "Amita Soni",
    "D. Choudhuri"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "An existence of a nontrivial solution in some `weaker' sense of the following system of equations \\begin{align*} (-\\Delta)^{s}u+l(x)\\phi u+w(x)|u|^{k-1}u&=\\mu~\\text{in}~\\Omega\\nonumber\\\\ (-\\Delta)^{s}\\phi&= l(x)u^2~\\text{in}~\\Omega\\nonumber\\\\ u=\\phi&=0 ~\\text{in}~\\mathbb{R}^N\\setminus\\Omega \\end{align*} has been proved. Here $s \\in (0,1)$, $l,w$ are bounded nonnegative functions in $\\Omega$, $\\mu$ is a Radon measure and $k > 1$ belongs to a certain range.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-04T13:31:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J35",
      "35J60"
    ],
    "keywords": [
      "radon measure",
      "fractional laplacians",
      "nontrivial solution",
      "bounded nonnegative functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}