{
  "id": "2206.10001",
  "version": "v1",
  "published": "2022-06-20T20:56:03.000Z",
  "updated": "2022-06-20T20:56:03.000Z",
  "title": "Nodal solutions for the weighted biharmonic equation with critical exponential growth",
  "authors": [
    "Brahim Dridi",
    "Rachaid Jaidane"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2201.09858, arXiv:2201.10433",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we deal with the logarithmic weighted fourth order elliptic equation in the unit disk of $B\\subset\\R^{4}$: $$\\displaystyle(P_{\\lambda})~~\\Delta(w(x) \\Delta u) = \\lambda\\ f(x,u) \\quad\\mbox{ in }\\quad B, \\quad u=\\frac{\\partial u}{\\partial n} \\quad\\mbox{ on } \\quad\\partial B,$$ where the nonlinearity $f$ is assumed to have exponential critical growth in view of Adam's type inequalities. By using the constrained minimization in Nehari set combined with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions to the problem $(P_{\\lambda})$ .",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-20T20:56:03.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical exponential growth",
      "weighted biharmonic equation",
      "nodal solutions",
      "logarithmic weighted fourth order elliptic",
      "weighted fourth order elliptic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}