{
  "id": "1110.2539",
  "version": "v1",
  "published": "2011-10-12T00:33:45.000Z",
  "updated": "2011-10-12T00:33:45.000Z",
  "title": "Super Polyharmonic Property of Solutions for PDE Systems and Its Applications",
  "authors": [
    "Wenxiong Chen",
    "Congming Li"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper, we prove that all the positive solutions for the PDE system (-\\Delta)^{k}u_{i} = f_{i}(u_{1},..., u_{m}), x \\in R^{n}, i = 1, 2,..., m are super polyharmonic, i.e. (-\\Delta)^{j}u_{i} > 0, j = 1, 2,..., k - 1; i = 1, 2,...,m. To prove this important super polyharmonic property, we introduced a few new ideas and derived some new estimates. As an interesting application, we establish the equivalence between the integral system u_{i}(x) = \\int_{R^{n}} \\frac{1}{|x - y|^{n-\\alpha}}f_{i}(u_{1}(y),..., u_{m}(y))dy, x \\in R^{n} and PDE system when \\alpha? = 2k < n",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-10-12T00:33:45.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "pde system",
      "important super polyharmonic property",
      "integral system",
      "positive solutions",
      "interesting application"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1110.2539C"
    }
  }
}