- Research Article
- Open Access
Nonexistence of Positive Solution for Quasilinear Elliptic Problems in the Half-Space
Journal of Inequalities and Applications volume 2007, Article number: 065126 (2007)
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.
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.
Gidas B, Spruck J: A priori bounds for positive solutions of nonlinear elliptic equations. Communications in Partial Differential Equations 1981,6(8):883–901. 10.1080/03605308108820196
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.2001.4029
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.2003.10.021
Serrin J: Local behavior of solutions of quasi-linear equations. Acta Mathematica 1964,111(1):247–302. 10.1007/BF02391014
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/BF02392645
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.3160200406
Bidaut-Véron M-F, Pohozaev SI: Nonexistence results and estimates for some nonlinear elliptic problems. Journal d'Analyse Mathématique 2001, 84: 1–49.
About this article
Cite this article
Lorca, S. Nonexistence of Positive Solution for Quasilinear Elliptic Problems in the Half-Space. J Inequal Appl 2007, 065126 (2007). https://doi.org/10.1155/2007/65126
- Bounded Domain
- Elliptic Problem
- Nonexistence Result
- Quasilinear Elliptic Problem