{
  "id": "1808.03674",
  "version": "v1",
  "published": "2018-08-10T18:58:22.000Z",
  "updated": "2018-08-10T18:58:22.000Z",
  "title": "Infinitely many solutions for a Hénon-type system in hyperbolic space",
  "authors": [
    "Patrícia Leal da Cunha",
    "Flávio Almeida Lemos"
  ],
  "comment": "12 pages",
  "categories": [
    "math.AP"
  ],
  "abstract": "This paper is devoted to study the semilinear elliptic system of H\\'enon-type \\begin{eqnarray*} -\\Delta_{\\mathbb{B}^{N}}u= K(d(x))Q_{u}(u,v) \\\\ -\\Delta_{\\mathbb{B}^{N}}v= K(d(x))Q_{v}(u,v) \\end{eqnarray*} in the hyperbolic space $\\mathbb{B}^{N}$, $N\\geq 3$, where $u, v \\in H_{r}^{1}(\\mathbb{B}^{N})=\\{\\phi\\in H^1(\\mathbb{B}^N): \\phi\\, \\text{is radial}\\}$ and $-\\Delta_{\\mathbb{B}^{N}}$ denotes the Laplace-Beltrami operator on $\\mathbb{B}^N$, $Q \\in C^{1}(\\mathbb{R}\\times \\mathbb{R},\\mathbb{R})$ is a p-homogeneous function, $d(x)=d_{\\mathbb{B}^N}(0,x)$ and $K\\geq0 $ is a continuous function. We prove a compactness result and together with the Clark's theorem we establish the existence of infinitely many solutions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-08-10T18:58:22.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "hyperbolic space",
      "hénon-type system",
      "semilinear elliptic system",
      "laplace-beltrami operator",
      "compactness result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}