{
  "id": "1603.05946",
  "version": "v1",
  "published": "2016-03-18T18:02:16.000Z",
  "updated": "2016-03-18T18:02:16.000Z",
  "title": "Existence of multi-bump solutions to biharmonic operator with critical exponential growth in $\\mathbb{R}^4$",
  "authors": [
    "Alânnio B. Nóbrega",
    "Denilson S. Pereira"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1602.03112",
  "categories": [
    "math.AP"
  ],
  "abstract": "Using variational methods, we establish existence of multi-bump solutions for the following class of problems $$ \\left\\{ \\begin{array}{l} \\Delta^2 u +(\\lambda V(x)+1)u = f(u), \\quad \\mbox{in} \\quad \\mathbb{R}^{4}, u \\in H^{2}(\\mathbb{R}^{4}), \\end{array} \\right. $$ where $\\Delta^2$ is the biharmonic operator, $f$ is a continuous function with critical exponential growth and $V : \\mathbb{R}^4 \\rightarrow \\mathbb{R}$ is a continuous function verifying some conditions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-03-18T18:02:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponential growth",
      "multi-bump solutions",
      "biharmonic operator",
      "continuous function",
      "variational methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160305946N"
    }
  }
}