{
  "id": "1605.07484",
  "version": "v1",
  "published": "2016-05-24T14:44:18.000Z",
  "updated": "2016-05-24T14:44:18.000Z",
  "title": "A natural constraint approach to normalized solutions of nonlinear Schrödinger equations and systems",
  "authors": [
    "Thomas Bartsch",
    "Nicola Soave"
  ],
  "comment": "29 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We prove existence of normalized solutions to \\[ \\begin{cases} -\\Delta u - \\lambda_1 u = \\mu_1 u^3+ \\beta u v^2 & \\text{in $\\mathbb{R}^3$} \\\\ -\\Delta v- \\lambda_2 v = \\mu_2 v^3 +\\beta u^2 v & \\text{in $\\mathbb{R}^3$}\\\\ \\int_{\\mathbb{R}^3} u^2 = a_1^2 \\quad \\text{and} \\quad \\int_{\\mathbb{R}^3} v^2 = a_2^2 \\end{cases} \\] for any $\\mu_1,\\mu_2,a_1,a_2>0$ and $\\beta<0$ prescribed. The approach is based upon the introduction of a natural constraint associated to the problem. Our method can be adapted to the scalar NLS equation with normalization constraint, and leads to alternative and simplified proofs to some results already available in the literature.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-24T14:44:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear schrödinger equations",
      "natural constraint approach",
      "normalized solutions",
      "scalar nls equation",
      "normalization constraint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}