{
  "id": "2102.10379",
  "version": "v1",
  "published": "2021-02-20T16:18:27.000Z",
  "updated": "2021-02-20T16:18:27.000Z",
  "title": "Elliptic problem involving a Choquard logarithmic term, singularity and a nonlinearity with exponential critical growth",
  "authors": [
    "Debajyoti Choudhuri"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "The existence and multiplicity of nontrivial solutions to the following problem \\begin{align*} \\begin{split} (-\\Delta)^{\\frac{1}{2}}u+u+(\\ln|\\cdot|*|u|^2)&=f(u)+\\mu|u|^{-\\gamma-1}u,~\\text{in}~\\mathbb{R} \\end{split} \\end{align*} will be proved. Here $\\mu>0$. we will show the existence of a nontrivial solution at a certain mountain pass level and another ground state solution when the nonlinearity is of exponential critical growth.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-20T16:18:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential critical growth",
      "choquard logarithmic term",
      "elliptic problem",
      "nonlinearity",
      "singularity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}