{
  "id": "1506.01669",
  "version": "v1",
  "published": "2015-06-04T18:04:03.000Z",
  "updated": "2015-06-04T18:04:03.000Z",
  "title": "Multiplicity and concentration of positive solutions for a class of quasilinear problems through Orlicz-Sobolev space",
  "authors": [
    "Claudianor O. Alves",
    "Ailton R. Silva"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we study existence, multiplicity and concentration of positive solutions for the following class of quasilinear problems \\[ - \\Delta_{\\Phi}u + V(\\epsilon x)\\phi(\\vert u\\vert)u = f(u)\\quad \\mbox{in} \\quad \\mathbb{R}^{N} \\,\\,\\, ( N\\geq 2 ), \\] where $\\Phi(t) = \\int_{0}^{\\vert t\\vert}\\phi(s)sds$ is a N-function, $ \\Delta_{\\Phi}$ is the $\\Phi$-Laplacian operator, $\\epsilon$ is a positive parameter, $V : \\mathbb{R}^{N} \\rightarrow \\mathbb{R} $ is a continuous function and $f : \\mathbb{R} \\rightarrow \\mathbb{R} $ is a $C^{1}$-function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-06-04T18:04:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "quasilinear problems",
      "positive solutions",
      "orlicz-sobolev space",
      "multiplicity",
      "concentration"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150601669A"
    }
  }
}