{
  "id": "1210.0782",
  "version": "v1",
  "published": "2012-10-02T14:16:18.000Z",
  "updated": "2012-10-02T14:16:18.000Z",
  "title": "A Reduction Method for Semilinear Elliptic Equations and Solutions Concentrating on Spheres",
  "authors": [
    "Filomena Pacella",
    "P. N. Srikanth"
  ],
  "doi": "10.1016/j.jfa.2014.03.004",
  "categories": [
    "math.AP"
  ],
  "abstract": "We show that any general semilinear elliptic problem with Dirichlet or Neumann boundary conditions in an annulus A in R^2m ;m >1, invariant by the action of a certain symmetry group can be reduced to a nonhomogenous similar problem in an annulus D in R^(m+1), invariant by another related symmetry. We apply this result to prove the existence of positive and sign changing solutions of a singularly perturbed elliptic problem in A which concentrate on one or two (m-1) dimensional spheres. We also prove that the Morse indices of these solutions tend to infinity as the parameter of concentration tends to infinity.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-10-02T14:16:18.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J61",
      "35B25",
      "35B40"
    ],
    "keywords": [
      "semilinear elliptic equations",
      "reduction method",
      "solutions concentrating",
      "general semilinear elliptic problem",
      "neumann boundary conditions"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1210.0782P"
    }
  }
}