Gradient estimates for a nonlinear elliptic equation on complete Riemannian manifolds

Bingqing Ma, Guangyue Huang

Published 2017-10-26Version 1

In this short note, we consider gradient estimates for positive solutions to the following nonlinear elliptic equation on a complete Riemannian manifold: $$\Delta u+\lambda u^{p}=0,$$ where $\lambda,p$ are two real constants and $\lambda\neq 0$. As an application, a Liouville type result is attained in some appropriate conditions.