{
  "id": "math/0303242",
  "version": "v1",
  "published": "2003-03-19T18:03:59.000Z",
  "updated": "2003-03-19T18:03:59.000Z",
  "title": "Existence result for a Neumann problem",
  "authors": [
    "Nikolaos Halidias"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we are going to show the existence of a nontrivial solution to the following model problem, $\\{\\begin{array}{lll} - \\Delta (u) = 2uln(1+u^2)+\\frac{|u|^2}{1+u^2}2u+usin(u) {a.e. on} \\Omega \\frac{\\partial u}{\\partial \\eta} = 0 {a.e. on} \\partial \\Omega. \\end{array} \\}$ As one can see the right hand side is superlinear. But we can not use an Ambrosetti-Rabinowitz condition in order to obtain that the corresponding energy functional satisfies (PS) condition. However, it follows that the energy functional satisfies the Cerami (PS) condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2003-03-19T18:03:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15"
    ],
    "keywords": [
      "neumann problem",
      "existence result",
      "corresponding energy functional satisfies",
      "right hand side",
      "nontrivial solution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......3242H"
    }
  }
}