{
  "id": "1509.07595",
  "version": "v1",
  "published": "2015-09-25T06:22:51.000Z",
  "updated": "2015-09-25T06:22:51.000Z",
  "title": "Uniqueness of positive solutions of a $n$-Laplace equation in a ball in $\\mathbb{r}^n$ with exponential nonlinearity",
  "authors": [
    "Adimurthi",
    "Karthik A",
    "Jacques Giacomoni"
  ],
  "categories": [
    "math.AP",
    "math.CA"
  ],
  "abstract": "Let $n \\geq 2$ and $\\Omega \\subset \\mathbb{R}^n$ be a bounded domain. Then by Trudinger-Moser embedding, $W_0^{1,n}(\\Omega)$ is embedded in an Orlicz space consisting of exponential functions. Consider the corresponding semi linear $n$-Laplace equation with critical or sub-critical exponential nonlinearity in a ball $B(R)$ with dirichlet boundary condition. In this paper, we prove that under suitable growth conditions on the nonlinearity, there exists an $\\gamma_0 > 0$, and a corresponding $R_0(\\gamma_0 ) > 0$ such that for all $0 < R < R_0$ , the problem admits a unique non degenerate positive radial solution $u$ with $\\|u\\|_{\\infty}\\geq \\gamma_0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-09-25T06:22:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "exponential nonlinearity",
      "laplace equation",
      "positive solutions",
      "non degenerate positive radial solution",
      "unique non degenerate positive radial"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}