{
  "id": "1510.06926",
  "version": "v1",
  "published": "2015-10-23T13:05:14.000Z",
  "updated": "2015-10-23T13:05:14.000Z",
  "title": "Concentration phenomena for fractional elliptic equations involving exponential critical growth",
  "authors": [
    "Claudianor O. Alves",
    "João Marcos do Ó",
    "Olímpio H. Miyagaki"
  ],
  "comment": "20 pages. arXiv admin note: text overlap with arXiv:1508.03964",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we deal with the following singular perturbed fractional elliptic problem $ \\epsilon^{} (-\\Delta)^{1/2}{u}+V(z)u=f(u)\\,\\,\\, \\mbox{in} \\,\\,\\, \\mathbb{R}, $ where $ (-\\Delta)^{1/2}u$ is the square root of the Laplacian and $f(s)$ has exponential critical growth. Under suitable conditions on $f(s)$, we construct a localized bound state solution concentrating at an isolated component of the positive local minimum points of the potential of $V$ as $\\epsilon$ goes to $0.$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-10-23T13:05:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "35B09",
      "35B33",
      "35R11",
      "G.1.8"
    ],
    "keywords": [
      "exponential critical growth",
      "fractional elliptic equations",
      "concentration phenomena",
      "bound state solution concentrating",
      "singular perturbed fractional elliptic problem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151006926A"
    }
  }
}