{
  "id": "1406.6242",
  "version": "v2",
  "published": "2014-06-24T14:09:11.000Z",
  "updated": "2016-01-03T20:10:36.000Z",
  "title": "$N$-Laplacian problems with critical Trudinger-Moser nonlinearities",
  "authors": [
    "Yang Yang",
    "Kanishka Perera"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove existence and multiplicity results for a $N$-Laplacian problem with a critical exponential nonlinearity that is a natural analog of the Brezis-Nirenberg problem for the borderline case of the Sobolev inequality. This extends results in the literature for the semilinear case $N = 2$ to all $N \\ge 2$. When $N > 2$ the nonlinear operator $- \\Delta_N$ has no linear eigenspaces and hence this extension requires new abstract critical point theorems that are not based on linear subspaces. We prove new abstract results based on the ${\\mathbb Z}_2$-cohomological index and a related pseudo-index that are applicable here.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-06-24T14:09:11.000Z",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2016-01-03T20:10:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35B33",
      "58E05"
    ],
    "keywords": [
      "critical trudinger-moser nonlinearities",
      "laplacian problem",
      "abstract critical point theorems",
      "multiplicity results",
      "natural analog"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1406.6242Y"
    }
  }
}