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Liouville theorems for nonlinear elliptic equations in half-spaces

  • Jorge García-MeliánEmail author
  • Alexander Quaas
  • Boyan Sirakov
Article

Abstract

In this paper we study the existence of nonnegative supersolutions of the nonlinear elliptic problem −Δu + |∇u|q = λup in the half-space ℝN+, where N = 2, q > 1, p > 0 and λ > 0. We obtain Liouville theorems for positive, bounded supersolutions, depending on the exponents q and p, the dimension N, and, in some critical cases, also on the parameter λ > 0.

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Acknowledgements

J. G.-M. and A. Q. were partially supported by Ministerio de Economía y Competitividad under grants MTM2011-27998 and MTM2014-52822-P (Spain). A. Q. was also partially supported by Fondecyt Grant No. 1151180 Programa Basal, CMM. U. de Chile and Millennium Nucleus Center for Analysis of PDE NC130017.

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Copyright information

© The Hebrew University of Jerusalem 2019

Authors and Affiliations

  • Jorge García-Melián
    • 1
    Email author
  • Alexander Quaas
    • 2
  • Boyan Sirakov
    • 3
  1. 1.Departamento de Análisis Matemático and Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atómica, Molecular y FotónicaUniversidad de La LagunaLa LagunaSpain
  2. 2.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile
  3. 3.Departamento de MatemáticaPontifícia Universidade Católica do Rio de JaneiroRio De JaneiroBrasil

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