{
  "id": "1604.06861",
  "version": "v1",
  "published": "2016-04-23T05:10:49.000Z",
  "updated": "2016-04-23T05:10:49.000Z",
  "title": "Stability and instability of standing waves for a generalized Choquard equation with potential",
  "authors": [
    "Zhipeng Cheng",
    "Minbo Yang"
  ],
  "comment": "29",
  "categories": [
    "math.AP"
  ],
  "abstract": "We are going to study the standing waves for a generalized Choquard equation with potential: $$ -i\\partial_t u-\\Delta u+V(x)u=(|x|^{-\\mu}\\ast|u|^p)|u|^{p-2}u, \\ \\ \\hbox{in}\\ \\ \\mathbb{R}\\times\\mathbb{R}^3, $$ where $V(x)$ is a real function, $0<\\mu<3$, $2-\\mu/3<p<6-\\mu$ and $\\ast$ stands for convolution. Under suitable assumptions on the potential and appropriate frequency $\\omega$ , the stability and instability of the standing waves $u=e^{i \\omega t}\\varphi(x)$ are investigated .",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-23T05:10:49.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "generalized choquard equation",
      "standing waves",
      "instability",
      "real function",
      "appropriate frequency"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160406861C"
    }
  }
}