{
  "id": "1907.04520",
  "version": "v1",
  "published": "2019-07-10T05:55:06.000Z",
  "updated": "2019-07-10T05:55:06.000Z",
  "title": "An elliptic partial differential equation and its application",
  "authors": [
    "Dragos-Patru Covei",
    "Traian A. Pirvu"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper deals with the following elliptic equation \\begin{equation*} -2\\left\\vert \\sigma \\right\\vert ^{2}\\Delta z+\\left\\vert \\nabla z\\right\\vert ^{2}+4\\alpha z=4\\left\\vert x\\right\\vert ^{2}\\text{ for }x\\in \\mathbb{R}^{N}% \\text{, (}N\\geq 1\\text{),} \\end{equation*}% where $\\alpha >0$ is a real parameter and $\\sigma $ is a vector from $% \\mathbb{R}^{N}$. The solution method is based on the sub- and super-solutions method. The case $N>1$ seemed not considered before. This equation models a stochastic production planning problem.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-10T05:55:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic partial differential equation",
      "application",
      "stochastic production planning problem",
      "real parameter",
      "solution method"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}