{
  "id": "1504.06144",
  "version": "v1",
  "published": "2015-04-23T12:35:23.000Z",
  "updated": "2015-04-23T12:35:23.000Z",
  "title": "Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations",
  "authors": [
    "Daomin Cao",
    "Shuanglong Li",
    "Peng Luo"
  ],
  "comment": "28pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We are concerned with the following nonlinear Schr\\\"odinger equation \\begin{equation*} -\\varepsilon^2\\Delta u+ V(x)u=|u|^{p-2}u,~u\\in H^1(\\R^N), \\end{equation*} where $N\\geq 3$, $2<p<\\frac{2N}{N-2}$. For $\\varepsilon$ small enough and a class of $V(x)$, we show the uniqueness of positive multi-bump solutions concentrating at $k$ different critical points of $V(x)$ under certain assumptions on asymptotic behavior of $V(x)$ and its first derivatives near those points. The degeneracy of critical points is allowed in this paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-04-23T12:35:23.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear schrödinger equations",
      "positive bound states",
      "uniqueness",
      "critical points",
      "positive multi-bump solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150406144C"
    }
  }
}