{
  "id": "1309.2810",
  "version": "v2",
  "published": "2013-09-11T12:50:05.000Z",
  "updated": "2015-02-15T12:20:29.000Z",
  "title": "Positive solutions of a class of semilinear equations with absorption and schrödinger equations",
  "authors": [
    "Alano Ancona",
    "Moshe Marcus"
  ],
  "comment": "41 pages including an Appendix of 10 pages by the first author. In this second version some references and explanations have been added and some misprints corrected",
  "categories": [
    "math.AP"
  ],
  "abstract": "Several results about positive solutions -in a Lipschitz domain- of a nonlinear elliptic equation in a general form $ \\Delta u(x)-g(x,u(x))=0$ are proved, extending thus some known facts in the case of $ g(x,t)=t^q$, $q>1$, and a smooth domain. Our results include a characterization -in terms of a natural capacity- of a (conditional) removability property, a characterization of moderate solutions and of their boundary trace and a property relating arbitrary positive solutions to moderate solutions. The proofs combine techniques of non-linear p.d.e.\\ with potential theoretic methods with respect to linear Schr\\\"odinger equations. A general result describing the measures that are diffuse with respect to certain capacities is also established and used. The appendix by the first author provides classes of functions $g$ such that the nonnegative solutions of $ \\Delta u-g(.,u)=0$ has some \"good\" properties which appear in the paper.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-11T12:50:05.000Z",
      "comment": "39 pages including an Appendix of 10 pages by the first author",
      "journal": null,
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2015-02-15T12:20:29.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "31Cxx",
      "35H99"
    ],
    "keywords": [
      "semilinear equations",
      "schrödinger equations",
      "moderate solutions",
      "absorption",
      "nonlinear elliptic equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 41,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.2810A"
    }
  }
}