{
  "id": "1807.03961",
  "version": "v1",
  "published": "2018-07-11T06:26:33.000Z",
  "updated": "2018-07-11T06:26:33.000Z",
  "title": "Existence results for Schrödinger $p(x)$-Laplace equations involving critical growth in $\\mathbb{R}^N$",
  "authors": [
    "Ky Ho",
    "Yun-Ho Kim",
    "Inbo Sim"
  ],
  "comment": "26 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We establish some existence results for Schr\\\"odinger $p(x)$-Laplace equations in $\\mathbb{R}^N$ with various potentials and critical growth of nonlinearity that may occur on some nonempty set, although not necessarily the whole space $\\mathbb{R}^N$. The proofs are mainly based on concentration-compactness principles in a suitable weighted variable exponent Sobolev space and its imbeddings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-11T06:26:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J62",
      "35B33",
      "35J20",
      "35J25",
      "35J70",
      "46E35",
      "47J10"
    ],
    "keywords": [
      "laplace equations",
      "existence results",
      "critical growth",
      "schrödinger",
      "weighted variable exponent sobolev space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}