Boundary Value Problems
Volume 2007 (2007), Article ID 47218, 11 pages
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

Academic Editor: Shujie Li

Copyright © 2007 Leonelo Iturriaga and Sebastian Lorca. 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.


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.