{
  "id": "1510.01409",
  "version": "v1",
  "published": "2015-10-06T01:33:08.000Z",
  "updated": "2015-10-06T01:33:08.000Z",
  "title": "Multi-bump solutions for Choquard equation with deepening potential well",
  "authors": [
    "Claudianor O. Alves",
    "Alânnio B. Nóbrega",
    "Minbo Yang"
  ],
  "comment": "26pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the existence of multi-bump solutions to Choquard equation $$ \\begin{array}{ll} -\\Delta u + (\\lambda a(x)+1)u=\\displaystyle\\big(\\frac{1}{|x|^{\\mu}}\\ast |u|^p\\big)|u|^{p-2}u \\mbox{ in } \\,\\,\\, \\R^3, \\end{array} $$ where $\\mu \\in (0,3), p\\in(2, 6-\\mu)$, $\\lambda$ is a positive parameter and the nonnegative function $a(x)$ has a potential well $ \\Omega:=int (a^{-1}(0))$ consisting of $k$ disjoint bounded components $ \\Omega:=\\cup_{j=1}^{k}\\Omega_j$. We prove that if the parameter $\\lambda$ is large enough then the equation has at least $2^{k}-1$ multi-bump solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-06T01:33:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "35J20",
      "35J65"
    ],
    "keywords": [
      "multi-bump solutions",
      "choquard equation",
      "deepening potential",
      "disjoint bounded components"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151001409A"
    }
  }
}