TY - JOUR
AU1 - Qian, Bin
AB - Let 
$${(M^n,g)}$$



(

M
n

,
g
)



 be an n-dimensional complete Riemannian manifold. We consider Yau’s gradient estimates for positive solutions to the following nonlinear equation

$$\Delta u + au {\rm log} u=0$$



Δ
u
+
a
u

log

u
=
0



where a is a constant. As an application, we obtain the Liouville property for this equation in the case of a < 0. In addition, we illustrate, by giving concrete examples, that our results are sharp.
TI - Yau’s gradient estimates for a nonlinear elliptic equation
JF - Archiv der Mathematik
DO - 10.1007/s00013-016-0983-2
DA - 2016-10-19
UR - https://www.deepdyve.com/lp/springer-journals/yau-s-gradient-estimates-for-a-nonlinear-elliptic-equation-NlHm0p5b0u
SP - 427
EP - 435
VL - 108
IS - 4
DP - DeepDyve
ER -