{
  "id": "1602.01071",
  "version": "v1",
  "published": "2016-02-02T20:26:01.000Z",
  "updated": "2016-02-02T20:26:01.000Z",
  "title": "Asymmetric critical $p$-Laplacian problems",
  "authors": [
    "Kanishka Perera",
    "Yang Yang",
    "Zhitao Zhang"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1406.6242, arXiv:1411.2198",
  "categories": [
    "math.AP"
  ],
  "abstract": "We obtain nontrivial solutions for two types of critical $p$-Laplacian problems with asymmetric nonlinearities in a smooth bounded domain in ${\\mathbb R}^N,\\, N \\ge 2$. For $p < N$, we consider an asymmetric problem involving the critical Sobolev exponent $p^\\ast = Np/(N - p)$. In the borderline case $p = N$, we consider an asymmetric critical exponential nonlinearity of the Trudinger-Moser type. In the absence of a suitable direct sum decomposition, we use a linking theorem based on the ${\\mathbb Z}_2$-cohomological index to obtain our solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-02T20:26:01.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35B33",
      "35J92",
      "35J20"
    ],
    "keywords": [
      "laplacian problems",
      "suitable direct sum decomposition",
      "asymmetric critical exponential nonlinearity",
      "smooth bounded domain",
      "asymmetric problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160201071P"
    }
  }
}