Boundary Value Problems 
Volume 2007 (2007), Article ID 47218, 11 pages
doi:10.1155/2007/47218
Research Article

Existence and Multiplicity Results for Degenerate Elliptic Equations with Dependence on the Gradient

Leonelo Iturriaga1 and Sebastian Lorca2

 1Departamento de Ingeniería Matemática y Centro de Modelamiento Matematico, Universidad de Chile, Casilla 170 Correo 3, Santiago 8370459, Chile
2Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica 1000007, Chile
Received 17 October 2006; Revised 2 January 2007; Accepted 9 February 2007

Recommended by Shujie Li

Abstract

We study the existence of positive solutions for a class of degenerate nonlinear elliptic equations with gradient dependence. For this purpose, we combine a blowup argument, the strong maximum principle, and Liouville-type theorems to obtain a priori estimates.