{
  "id": "2011.07615",
  "version": "v1",
  "published": "2020-11-15T19:40:53.000Z",
  "updated": "2020-11-15T19:40:53.000Z",
  "title": "Ground states of elliptic problems over cones",
  "authors": [
    "Giovany M. Figueiredo",
    "Humberto Ramos Quoirin",
    "Kaye Silva"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Given a reflexive Banach space $X$, we consider a class of functionals $\\Phi \\in C^1(X,\\Re)$ that do not behave in a uniform way, in the sense that the map $t \\mapsto \\Phi(tu)$, $t>0$, does not have a uniform geometry with respect to $u\\in X$. Assuming instead such a uniform behavior within an open cone $Y \\subset X \\setminus \\{0\\}$, we show that $\\Phi$ has a ground state relative to $Y$. Some further conditions ensure that this relative ground state is the (absolute) ground state of $\\Phi$. Several applications to elliptic equations and systems are given.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-15T19:40:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elliptic problems",
      "uniform behavior",
      "open cone",
      "uniform geometry",
      "reflexive banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}