$G$ is a region contained in upper half plane of $\mathbb{R}^2$, that is, for every point $(x,y)$ in $G$ we have $y>0$.
If $u$ is a solution of the equation $yu_{xx}+u_{yy}=0$, show that $u$ couldn't attain its maximum in interior of $G$, if $u$ is not a constant.
I have no idea. Thanks for help.