{
  "id": "2105.11379",
  "version": "v1",
  "published": "2021-05-24T16:16:40.000Z",
  "updated": "2021-05-24T16:16:40.000Z",
  "title": "New multiplicity results for critical $p$-Laplacian problems",
  "authors": [
    "Carlo Mercuri",
    "Kanishka Perera"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove new multiplicity results for the Brezis-Nirenberg problem for the $p$-Laplacian. Our proofs are based on a new abstract critical point theorem involving the ${\\mathbb Z}_2$-cohomological index that requires less compactness than the (PS) condition. Some of our results are new even in the semilinear case $p = 2$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-24T16:16:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J92",
      "35B33",
      "58E05"
    ],
    "keywords": [
      "multiplicity results",
      "laplacian problems",
      "abstract critical point theorem",
      "brezis-nirenberg problem",
      "semilinear case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}