{
  "id": "1801.09925",
  "version": "v1",
  "published": "2018-01-30T10:41:37.000Z",
  "updated": "2018-01-30T10:41:37.000Z",
  "title": "Multiplicity results for $(p,\\, q)$ fractional elliptic equations involving critical nonlinearities",
  "authors": [
    "Mousomi Bhakta",
    "Debangana Mukherjee"
  ],
  "comment": "34 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we prove the existence of infinitely many nontrivial solutions for the class of $(p,\\, q)$ fractional elliptic equations involving concave-critical nonlinearities in bounded domains in $\\mathbb{R}^N$. Further, when the nonlinearity is of convex-critical type, we establish the multiplicity of nonnegative solutions using variational methods. In particular, we show the existence of at least $cat_{\\Omega}(\\Omega)$ nonnegative solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-30T10:41:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional elliptic equations",
      "nonlinearity",
      "multiplicity results",
      "nonnegative solutions",
      "variational methods"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 34,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}