{
  "id": "1807.07442",
  "version": "v1",
  "published": "2018-07-18T10:44:27.000Z",
  "updated": "2018-07-18T10:44:27.000Z",
  "title": "Concentration phenomena for a fractional Choquard equation with magnetic field",
  "authors": [
    "Vincenzo Ambrosio"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:1801.00199",
  "journal": "Dynamics of Partial Differential Equations (2018)",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the following nonlinear fractional Choquard equation $$ \\varepsilon^{2s}(-\\Delta)^{s}_{A/\\varepsilon} u + V(x)u = \\varepsilon^{\\mu-N}\\left(\\frac{1}{|x|^{\\mu}}*F(|u|^{2})\\right)f(|u|^{2})u \\mbox{ in } \\mathbb{R}^{N}, $$ where $\\varepsilon>0$ is a parameter, $s\\in (0, 1)$, $0<\\mu<2s$, $N\\geq 3$, $(-\\Delta)^{s}_{A}$ is the fractional magnetic Laplacian, $A:\\mathbb{R}^{N}\\rightarrow \\mathbb{R}^{N}$ is a smooth magnetic potential, $V:\\mathbb{R}^{N}\\rightarrow \\mathbb{R}$ is a positive potential with a local minimum and $f$ is a continuous nonlinearity with subcritical growth. By using variational methods we prove the existence and concentration of nontrivial solutions for $\\varepsilon>0$ small enough.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-18T10:44:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "concentration phenomena",
      "magnetic field",
      "nonlinear fractional choquard equation",
      "smooth magnetic potential",
      "fractional magnetic laplacian"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}