{
  "id": "1811.04044",
  "version": "v1",
  "published": "2018-11-09T17:59:53.000Z",
  "updated": "2018-11-09T17:59:53.000Z",
  "title": "Nonradial normalized solutions for nonlinear scalar field equations",
  "authors": [
    "Louis Jeanjean",
    "Sheng-Sen Lu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "We study the following nonlinear scalar field equation $$ -\\Delta u=f(u)-\\mu u, \\quad u \\in H^1(\\mathbb{R}^N) \\quad \\text{with} \\quad \\|u\\|^2_{L^2(\\mathbb{R}^N)}=m. $$ Here $f\\in C(\\mathbb{R},\\mathbb{R})$, $m>0$ is a given constant and $\\mu\\in\\mathbb{R}$ is a Lagrange multiplier. In a mass subcritical case but under general assumptions on the nonlinearity $f$, we show the existence of one nonradial solution for any $N\\geq4$, and obtain multiple (sometimes infinitely many) nonradial solutions when $N=4$ or $N\\geq6$. In particular, all these solutions are sign-changing.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-09T17:59:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60",
      "58E05"
    ],
    "keywords": [
      "nonlinear scalar field equation",
      "nonradial normalized solutions",
      "nonradial solution",
      "lagrange multiplier",
      "mass subcritical case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}