{
  "id": "2208.11103",
  "version": "v1",
  "published": "2022-08-23T17:25:30.000Z",
  "updated": "2022-08-23T17:25:30.000Z",
  "title": "Entire subsolutions of a kind of k-Hessian type equations with gradient terms",
  "authors": [
    "Jingwen Ji",
    "Feida Jiang",
    "Mengni Li"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we consider a kind of $k$-Hessian type equations $S_k^{\\frac{1}{k}}(D^2u+\\mu|D u|I)= f(u)$ in $\\mathbb{R}^n$, and provide a necessary and sufficient condition of $f$ on the existence and nonexistence of entire admissible subsolutions, which can be regarded as a generalized Keller-Osserman condition. The existence and nonexistence results are proved in different ranges of the parameter $\\mu$ respectively, which embrace the standard Hessian equation case ($\\mu=0$) by Ji and Bao (Proc Amer Math Soc 138: 175--188, 2010) as a typical example. The difference between the semilinear case ($k=1$) and the fully nonlinear case ($k\\ge 2$) is also concerned.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-23T17:25:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J60"
    ],
    "keywords": [
      "k-hessian type equations",
      "entire subsolutions",
      "gradient terms",
      "proc amer math soc",
      "standard hessian equation case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}