{
  "id": "0708.1155",
  "version": "v2",
  "published": "2007-08-08T18:35:53.000Z",
  "updated": "2007-08-14T00:26:26.000Z",
  "title": "\"Boundary blowup\" type sub-solutions to semilinear elliptic equations with Hardy potential",
  "authors": [
    "Catherine Bandle",
    "Vitaly Moroz",
    "Wolfgang Reichel"
  ],
  "comment": "23 pages, 3 figures",
  "categories": [
    "math.AP"
  ],
  "abstract": "Semilinear elliptic equations which give rise to solutions blowing up at the boundary are perturbed by a Hardy potential. The size of this potential effects the existence of a certain type of solutions (large solutions): if the potential is too small, then no large solution exists. The presence of the Hardy potential requires a new definition of large solutions, following the pattern of the associated linear problem. Nonexistence and existence results for different types of solutions will be given. Our considerations are based on a Phragmen-Lindelof type theorem which enables us to classify the solutions and sub-solutions according to their behavior near the boundary. Nonexistence follows from this principle together with the Keller-Osserman upper bound. The existence proofs rely on sub- and super-solution techniques and on estimates for the Hardy constant derived in Marcus, Mizel and Pinchover.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-08-14T00:26:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35J70",
      "31B25"
    ],
    "keywords": [
      "semilinear elliptic equations",
      "hardy potential",
      "boundary blowup",
      "type sub-solutions",
      "large solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.1155B"
    }
  }
}