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