Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds

Ma, Bingqing; Huang, Guangyue; Luo, Yong

doi:10.1090/proc/14106

Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds
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by Bingqing Ma, Guangyue Huang and Yong Luo PDF

Proc. Amer. Math. Soc. 146 (2018), 4993-5002 Request permission

Abstract:

In this short paper, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: \begin{equation*} \Delta u+cu^{\alpha }=0, \end{equation*} where $c, \alpha$ are two real constants and $c\neq 0$.

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