{
  "id": "2403.18014",
  "version": "v1",
  "published": "2024-03-26T18:02:02.000Z",
  "updated": "2024-03-26T18:02:02.000Z",
  "title": "Generalized Chern-Simons-Schrodinger system with critical exponential growth: the zero mass case",
  "authors": [
    "Liejun Shen",
    "Marco Squassina"
  ],
  "comment": "20 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "We consider the existence of ground state solutions for a class of zero-mass Chern-Simons-Schr\\\"{o}dinger systems \\[ \\left\\{ \\begin{array}{ll} \\displaystyle -\\Delta u +A_0 u+\\sum\\limits_{j=1}^2A_j^2 u=f(u)-a(x)|u|^{p-2}u, \\newline \\displaystyle \\partial_1A_2-\\partial_2A_1=-\\frac{1}{2}|u|^2,~\\partial_1A_1+\\partial_2A_2=0, \\newline \\displaystyle \\partial_1A_0=A_2|u|^2,~ \\partial_2A_0=-A_1|u|^2, \\end{array} \\right. \\] where $a:\\mathbb R^2\\to\\mathbb R^+$ is an external potential, $p\\in(1,2)$ and $f\\in \\mathcal{C}(\\mathbb R)$ denotes a nonlinearity that fulfills the critical exponential growth in the Trudinger-Moser sense at infinity. By introducing an improvement of the version of Trudinger-Moser inequality, we are able to investigate the existence of positive ground state solutions for the given system using variational method.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-03-26T18:02:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J20",
      "58E50",
      "35B06"
    ],
    "keywords": [
      "critical exponential growth",
      "zero mass case",
      "generalized chern-simons-schrodinger system",
      "positive ground state solutions",
      "variational method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}