{
  "id": "1805.06551",
  "version": "v1",
  "published": "2018-05-16T23:02:22.000Z",
  "updated": "2018-05-16T23:02:22.000Z",
  "title": "Ground state of a magnetic nonlinear Choquard equation",
  "authors": [
    "Hamilton Bueno",
    "Guido G. Mamani",
    "Gilberto A. Pereira"
  ],
  "comment": "11 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the stationary magnetic nonlinear Choquard equation \\[-(\\nabla+iA(x))^2u+ V(x)u=\\bigg(\\frac{1}{|x|^{\\alpha}}*F(|u|)\\bigg)\\frac{f(|u|)}{|u|}{u},\\] where $A: \\mathbb{R}^{N}\\rightarrow \\mathbb{R}^{N}$ is a vector potential, $V$ is a scalar potential, $f\\colon\\mathbb{R}\\to\\mathbb{R}$ and $F$ is the primitive of $f$. Under mild hypotheses, we prove the existence of a ground state solution for this problem. We also prove a simple multiplicity result by applying Ljusternik-Schnirelmann methods.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-16T23:02:22.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35Q55",
      "35Q40",
      "35J20"
    ],
    "keywords": [
      "stationary magnetic nonlinear choquard equation",
      "ground state solution",
      "simple multiplicity result",
      "scalar potential",
      "mild hypotheses"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}