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  • Research Article
  • Open Access

Nonexistence of Positive Solution for Quasilinear Elliptic Problems in the Half-Space

Journal of Inequalities and Applications20072007:065126

  • Received: 16 October 2006
  • Accepted: 9 February 2007
  • Published:


Liouville-type results in or in the half-space might be important to obtain a priori estimates for positive solutions of associated problems in bounded domains via some procedure of blow up. In this work, we obtain a nonexistence result for the positive solution of , in the half-space.


  • Bounded Domain
  • Elliptic Problem
  • Nonexistence Result
  • Quasilinear Elliptic Problem


Authors’ Affiliations

Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7-D, Arica, 1000007, Chile


  1. Mitidieri È, Pohozaev SI: Nonexistence of positive solutions for quasilinear elliptic problems in. Proceedings of the Steklov Institute of Mathematics 1999,227(4):186–216.MathSciNetGoogle Scholar
  2. Gidas B, Spruck J: A priori bounds for positive solutions of nonlinear elliptic equations. Communications in Partial Differential Equations 1981,6(8):883–901. 10.1080/03605308108820196MathSciNetView ArticleMATHGoogle Scholar
  3. Azizieh C, Clément P: A priori estimates and continuation methods for positive solutions of-Laplace equations. Journal of Differential Equations 2002,179(1):213–245. 10.1006/jdeq.2001.4029MathSciNetView ArticleMATHGoogle Scholar
  4. Ruiz D: A priori estimates and existence of positive solutions for strongly nonlinear problems. Journal of Differential Equations 2004,199(1):96–114. 10.1016/j.jde.2003.10.021MathSciNetView ArticleMATHGoogle Scholar
  5. Serrin J: Local behavior of solutions of quasi-linear equations. Acta Mathematica 1964,111(1):247–302. 10.1007/BF02391014MathSciNetView ArticleMATHGoogle Scholar
  6. Serrin J, Zou H: Cauchy-Liouville and universal boundedness theorems for quasilinear elliptic equations and inequalities. Acta Mathematica 2002,189(1):79–142. 10.1007/BF02392645MathSciNetView ArticleMATHGoogle Scholar
  7. Trudinger NS: On Harnack type inequalities and their application to quasilinear elliptic equations. Communications on Pure and Applied Mathematics 1967, 20: 721–747. 10.1002/cpa.3160200406MathSciNetView ArticleMATHGoogle Scholar
  8. Bidaut-Véron M-F, Pohozaev SI: Nonexistence results and estimates for some nonlinear elliptic problems. Journal d'Analyse Mathématique 2001, 84: 1–49.View ArticleMATHGoogle Scholar