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

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.

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Correspondence to Leonelo Iturriaga.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Iturriaga, L., Lorca, S. Existence and Multiplicity Results for Degenerate Elliptic Equations with Dependence on the Gradient. Bound Value Probl 2007, 047218 (2007). https://doi.org/10.1155/2007/47218

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