Elliptic equations with absorption in a half-space



We give a necessary and sufficient condition, in the spirit of the classical works by Keller and Osserman, for the elliptic equation Δu = f (u) to have a solution in a half-space of RN. The function f is supposed to be nondecreasing and nonnegative, and we are interested in solutions whose range is where f > 0. The possibility of obtaining such a necessary and sufficient condition has been an open question for a long time.


Elliptic equations non-existence half-space coercive problems subsolutions 

Mathematical subject classification

35J60 35J61 


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© Sociedade Brasileira de Matemática 2016

Authors and Affiliations

  1. 1.Departamento de AnálisisMatemáticoUniversidad de La LagunaLa LagunaSpain
  2. 2.Instituto Universitario de Estudios Avanzados (IUdEA) en Física Atómica, Molecular y FotónicaUniversidad de La LagunaLa LagunaSpain
  3. 3.Departamento de MatemáticaUniversidad Técnica Federico Santa María Casilla V-110, Avda. Espa na, 1680ValparaísoChile
  4. 4.Departamento de Matemática PUC-RioRio de JaneiroBrazil

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