{
  "id": "1701.04119",
  "version": "v1",
  "published": "2017-01-15T21:54:25.000Z",
  "updated": "2017-01-15T21:54:25.000Z",
  "title": "Liouville-type theorems with finite Morse index for Δ_λ-Laplace operator",
  "authors": [
    "Belgacem Rahal"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study solutions, possibly unbounded and sign-changing, of the following problem: -\\D_{\\lambda} u=|x|_{\\lambda}^a |u|^{p-1}u, in R^n,\\;n\\geq 1,\\; p>1, and a \\geq 0, where \\D_{\\lambda} is a strongly degenerate elliptic operator, the functions \\lambda=(\\lambda_1, ..., \\lambda_k) : R^n \\rightarrow R^k, satisfies some certain conditions, and |.|_{\\lambda} the homogeneous norm associated to the \\D_{\\lambda}-Laplacian. We prove various Liouville-type theorems for smooth solutions under the assumption that they are stable or stable outside a compact set of R^n. First, we establish the standard integralestimates via stability property to derive the nonexistence results for stable solutions. Next, by mean of the Pohozaev identity, we deduce the Liouville-type theorem for solutions stable outside a compact set.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-15T21:54:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite morse index",
      "liouville-type theorem",
      "compact set",
      "strongly degenerate elliptic operator",
      "study solutions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}