{
  "id": "0804.4030",
  "version": "v1",
  "published": "2008-04-25T01:18:59.000Z",
  "updated": "2008-04-25T01:18:59.000Z",
  "title": "Infinitely many solution for prescribed curvature problem on $S^N$",
  "authors": [
    "Juncheng Wei",
    "Shusen Yan"
  ],
  "comment": "40 pages",
  "journal": "Journal of Functional Analysis 258(2010)",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the following prescribed scalar curvature problem on $ S^N$ (*)$$\\left\\{\\begin{array}{l} - \\Delta_{S^N} u + \\frac{N(N-2)}{2} u = \\tilde{K} u^{\\frac{N+2}{N-2}} {on} S^N, u >0 \\end{array}\\right. $$ where $ \\tilde{K}$ is positive and rotationally symmetric. We show that if $\\tilde{K}$ has a local maximum point between the poles then equation (*) has {\\bf infinitely many non-radial positive} solutions, whose energy can be made arbitrarily large.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-04-25T01:18:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B20"
    ],
    "keywords": [
      "prescribed curvature problem",
      "prescribed scalar curvature problem",
      "local maximum point",
      "non-radial"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0804.4030W"
    }
  }
}