{
  "id": "1711.05711",
  "version": "v1",
  "published": "2017-11-15T18:17:15.000Z",
  "updated": "2017-11-15T18:17:15.000Z",
  "title": "Nonradial solutions of nonlinear scalar field equations",
  "authors": [
    "Jarosław Mederski"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove new results concerning the nonlinear scalar field equation \\begin{equation*} \\left\\{ \\begin{array}{ll} -\\Delta u = g(u)&\\quad \\hbox{in }\\mathbb{R}^N,\\; N\\geq 3,\\\\ u\\in H^1(\\mathbb{R}^N)& \\end{array} \\right. \\end{equation*} with a nonlinearity $g$ satisfying the general assumptions due to Berestycki and Lions. In particular, we find at least one nonradial solution for any $N\\geq 4$ minimizing the energy functional on the topological Pohozaev constraint. If in addition $N\\neq 5$, then there are infinitely many nonradial solutions. The results give a partial answer to an open question posed by Berestycki and Lions in [5,6]. Moreover, we build a critical point theory on a topological manifold, which enables us to solve the above equation as well as to treat new elliptic problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-15T18:17:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "58E05"
    ],
    "keywords": [
      "nonlinear scalar field equation",
      "nonradial solution",
      "general assumptions",
      "critical point theory",
      "berestycki"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}