Open Access

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

Journal of Inequalities and Applications20072007:065126

DOI: 10.1155/2007/65126

Received: 16 October 2006

Accepted: 9 February 2007

Published: 5 March 2007

Abstract

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.

[12345678]

Authors’ Affiliations

(1)
Instituto de Alta Investigación, Universidad de Tarapacá

References

  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

Copyright

© Sebastián Lorca 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.