{
  "id": "1204.2163",
  "version": "v1",
  "published": "2012-04-10T14:24:42.000Z",
  "updated": "2012-04-10T14:24:42.000Z",
  "title": "Existence of solution to a critical equation with variable exponent",
  "authors": [
    "Julián Fernández Bonder",
    "Nicolas Saintier",
    "Analía Silva"
  ],
  "journal": "Annales Academiae Scientiarum Fennicae Mathematica, 37 (2012), 579-594",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the existence problem for the $p(x)-$Laplacian operator with a nonlinear critical source. We find a local condition on the exponents ensuring the existence of a nontrivial solution that shows that the Pohozaev obstruction does not holds in general in the variable exponent setting. The proof relies on the Concentration--Compactness Principle for variable exponents and the Mountain Pass Theorem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-04-10T14:24:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35B33"
    ],
    "keywords": [
      "variable exponent",
      "critical equation",
      "mountain pass theorem",
      "local condition",
      "existence problem"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1204.2163F"
    }
  }
}