{
  "id": "math/0409153",
  "version": "v1",
  "published": "2004-09-09T09:31:56.000Z",
  "updated": "2004-09-09T09:31:56.000Z",
  "title": "Bubble towers for supercritical semilinear elliptic equations",
  "authors": [
    "Yuxin Ge",
    "Ruihua Jing",
    "Frank Pacard"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We construct positive solutions of the semilinear elliptic problem $\\Delta u+ \\lambda u + u^p = 0$ with Dirichet boundary conditions, in a bounded smooth domain $\\Omega \\subset \\R^N$ $(N\\geq 4)$, when the exponent $p$ is supercritical and close enough to $\\frac{N+2}{N-2}$ and the parameter $\\lambda\\in\\R$ is small enough. As $p\\to \\frac{N+2}{N-2}$, the solutions have multiple blow up at finitely many points which are the critical points of a function whose definition involves Green's function. Our result extends the result of Del Pino, Dolbeault and Musso \\cite{DDM} when $\\Omega$ is a ball and the solutions are radially symmetric.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-09-09T09:31:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J25"
    ],
    "keywords": [
      "supercritical semilinear elliptic equations",
      "bubble towers",
      "semilinear elliptic problem",
      "dirichet boundary conditions",
      "bounded smooth domain"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......9153G"
    }
  }
}