{
  "id": "2312.02718",
  "version": "v1",
  "published": "2023-12-05T12:33:40.000Z",
  "updated": "2023-12-05T12:33:40.000Z",
  "title": "Multiplicity of Positive Solutions of Nonlinear Elliptic Equation with Gradient Term",
  "authors": [
    "Fei Fang",
    "Zhong Tan",
    "Huiru Xiong"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider the following nonlinear elliptic equation with gradient term: \\[ \\left\\{ \\begin{gathered} - \\Delta u - \\frac{1}{2}(x \\cdot \\nabla u) + (\\lambda a(x)+b(x))u = \\beta u^q +u^{2^*-1}, \\hfill 0<u \\in {H_K^{1}(\\mathbb{R}^N)}, \\hfill \\\\ \\end{gathered} \\right . \\] where $\\lambda, \\beta \\in (0,\\infty), q \\in (1,2^*-1), 2^* = 2N/(N-2), N\\geq3, a(x), b(x): \\mathbb{R}^N \\to \\mathbb{R}$ are continuous functions, and $a(x)$ is nonnegative on $\\mathbb{R}^N$. When $\\lambda$ is large enough, we prove the existence and multiplicity of positive solutions to the equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-05T12:33:40.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nonlinear elliptic equation",
      "gradient term",
      "positive solutions",
      "multiplicity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}