{
  "id": "2409.05138",
  "version": "v1",
  "published": "2024-09-08T15:43:33.000Z",
  "updated": "2024-09-08T15:43:33.000Z",
  "title": "Some applications of the Nehari manifold method to functionals in $C^1(X \\setminus \\{0\\})$",
  "authors": [
    "Edir Junior Ferreira Leite",
    "Humberto Ramos Quoirin",
    "Kaye Silva"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "Given a real Banach space $X$, we show that the Nehari manifold method can be applied to functionals which are $C^1$ in $X \\setminus \\{0\\}$. In particular we deal with functionals that can be unbounded near $0$, and prove the existence of a ground state and infinitely many critical points for such functionals. These results are then applied to three classes of problems: the {\\it prescribed energy problem} for a family of functionals depending on a parameter, problems involving the {\\it affine} $p$-Laplacian operator, and degenerate Kirchhoff type problems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-08T15:43:33.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "nehari manifold method",
      "functionals",
      "degenerate kirchhoff type problems",
      "applications",
      "real banach space"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}