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Entire positive solutions of the singular Emden-Fowler equation with nonlinear gradient term

Teodora Liliana Dinu
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Abstract

Let $p$ and $q$ be locally Hölder functions in $\RR^N$, $p>0$ and $q\geq 0$. We study the Emden-Fowler equation $-Δu+ q(x)|\nabla u|^a=p(x)u^{-γ}$ in $\RR^N$, where $a$ and $γ$ are positive numbers. Our main result establishes that the above equation has a unique positive solutions decaying to zero at infinity. Our proof is elementary and it combines the maximum principle for elliptic equations with a theorem of Crandall, Rabinowitz and Tartar.

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Teodora Liliana Dinu. 2005-11-07. Entire positive solutions of the singular Emden-Fowler equation with nonlinear gradient term. https://arxiv.org/abs/math/0511164

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