{
  "id": "math/0304003",
  "version": "v1",
  "published": "2003-04-01T06:57:35.000Z",
  "updated": "2003-04-01T06:57:35.000Z",
  "title": "On Neumann superlinear elliptic problems",
  "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{equation*} \\left\\{\\begin{array}{lll} -\\Delta (u) = 2uln(1+u^2)+\\frac{|u|^2}{1+u^2}2u+u(sin(u)-cos(u)) \\mbox{a.e. on } \\Omega \\frac{\\partial u}{\\partial \\eta} = 0 {a.e. on} \\partial \\Omega. \\end{array} \\right. \\end{equation*} 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": "2003-04-01T06:57:35.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35A15"
    ],
    "keywords": [
      "neumann superlinear elliptic problems",
      "right hand side",
      "corresponding energy functional satisfies",
      "model problem",
      "ambrosetti-rabinowitz condition"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2003math......4003H"
    }
  }
}