{
  "id": "1204.1825",
  "version": "v1",
  "published": "2012-04-09T08:25:57.000Z",
  "updated": "2012-04-09T08:25:57.000Z",
  "title": "Schrödinger-Poisson equations with singular potentials in $R^3$",
  "authors": [
    "Yongsheng Jiang",
    "Huan-Song Zhou"
  ],
  "comment": "23pages",
  "doi": "10.1016/j.jmaa.2014.03.034",
  "categories": [
    "math.AP"
  ],
  "abstract": "The existence and $L^{\\infty}$ estimate of positive solutions are discussed for the following Schr\\\"{o}dinger-Poisson system {ll} -\\Delta u +(\\lambda+\\frac{1}{|y|^\\alpha})u+\\phi (x) u =|u|^{p-1}u, x=(y,z)\\in \\mathbb{R}^2\\times\\mathbb{R}, -\\Delta\\phi = u^2,\\ \\lim\\limits_{|x|\\rightarrow +\\infty}\\phi(x)=0, \\hfill y=(x_1,x_2) \\in \\mathbb{R}^2 with |y|=\\sqrt{x_1^2+x_2^2}, where $\\lambda\\geqslant0$, $\\alpha\\in[0,8)$ and $\\max\\{2,\\frac{2+\\alpha}{2}\\}<p<5$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-09T08:25:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "singular potentials",
      "schrödinger-poisson equations",
      "positive solutions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.1825J"
    }
  }
}