Solvability of nonlinear elliptic equations with gradient terms

2012/08/31 by Patricio Felmer, Alexander Quaas, Felmer, Patricio +3 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1208.6562

arxiv created 2012/08/31 · arxiv updated 2012/09/03

Abstract

We study the solvability in the whole Euclidean space of coercive quasi-linear and fully nonlinear elliptic equations modeled on Δu± g(|∇ u|)= f(u), u≥0, where f and g are increasing continuous functions. We give conditions on f and g which guarantee the availability or the absence of positive solutions of such equations in \R^N. Our results considerably improve the existing ones and are sharp or close to sharp in the model cases. In particular, we completely characterize the solvability of such equations when f and g have power growth at infinity. We also derive a solvability statement for coercive equations in general form.

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• Keller-Osserman and Harnack type results for nonlinear elliptic PDE with unbounded ingredients

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