{
  "id": "2206.10615",
  "version": "v1",
  "published": "2022-06-20T21:07:48.000Z",
  "updated": "2022-06-20T21:07:48.000Z",
  "title": "Nodal solutions for Logarithmic weighted $N$-Laplacian problem with exponential nonlinearities",
  "authors": [
    "Brahim Dridi",
    "Rached Jaidane"
  ],
  "comment": "arXiv admin note: substantial text overlap with arXiv:2206.10001",
  "categories": [
    "math.AP"
  ],
  "abstract": "In this article, we study the following problem $$-{\\rm div} (\\omega(x)|\\nabla u|^{N-2} \\nabla u) = \\lambda\\ f(x,u) \\quad\\mbox{ in }\\quad B, \\quad u=0 \\quad\\mbox{ on } \\quad\\partial B,$$ where $B$ is the unit ball of $\\mathbb{R^{N}}$, $N\\geq2$ and $ w(x)$ a singular weight of logarithm type. The reaction source $f(x,u)$ is a radial function with respect to $x$ and is subcritical or critical with respect to a maximal growth of exponential type. By using the constrained minimization in Nehari set coupled with the quantitative deformation lemma and degree theory, we prove the existence of nodal solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-20T21:07:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nodal solutions",
      "laplacian problem",
      "exponential nonlinearities",
      "logarithmic",
      "singular weight"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}