{
  "id": "1410.2984",
  "version": "v1",
  "published": "2014-10-11T11:07:07.000Z",
  "updated": "2014-10-11T11:07:07.000Z",
  "title": "On a class of critical $(p,q)$-Laplacian problems",
  "authors": [
    "Pasquale Candito",
    "Salvatore A. Marano",
    "Kanishka Perera"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:1406.6242",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain nontrivial solutions of a critical $(p,q)$-Laplacian problem in a bounded domain. In addition to the usual difficulty of the loss of compactness associated with problems involving critical Sobolev exponents, this problem lacks a direct sum decomposition suitable for applying the classical linking theorem. We show that every Palais-Smale sequence at a level below a certain energy threshold admits a subsequence that converges weakly to a nontrivial critical point of the variational functional. Then we prove an abstract critical point theorem based on a cohomological index and use it to construct a minimax level below this threshold.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-11T11:07:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35B33",
      "58E05"
    ],
    "keywords": [
      "laplacian problem",
      "abstract critical point theorem",
      "energy threshold admits",
      "direct sum decomposition",
      "nontrivial solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.2984C"
    }
  }
}