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

Published: 5 April 2007

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.