Open Access Research Article

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

Leonelo Iturriaga1* and Sebastian Lorca2

Author Affiliations

1 Departamento de Ingeniería Matemática y Centro de Modelamiento Matematico, Universidad de Chile, Casilla 170 Correo 3, Santiago 8370459, Chile

2 Instituto de Alta Investigación, Universidad de Tarapacá, Casilla 7 D, Arica 1000007, Chile

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Boundary Value Problems 2007, 2007:047218  doi:10.1155/2007/47218

The electronic version of this article is the complete one and can be found online at:

Received:17 October 2006
Revisions received:2 January 2007
Accepted:9 February 2007
Published:5 April 2007

© 2007 Iturriaga and 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.


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