Complete Classification of the Euclidean Complete Solutions to a Monge-Ampere Equation

We study a Monge-Amp`{e}re equation with power term for some $p\in \mathbb{R}$. A solution $u$ is called to be Euclidean complete if it is an entire solution defined over the whole ${\mathbb{R}}^n$ or its graph is a large hypersurface satisfying the large condition $u(x)\to \mathrm{\infty }$ as $\mathrm{d}\mathrm{i}\mathrm{s}\mathrm{t}(x,\mathrm{\partial }\mathrm{\Omega })\to 0$ in case of $\mathrm{\Omega }≠{\mathbb{R}}^n$. In this paper, we will give various sharp conditions on $p$ and $\mathrm{\Omega }$ classifying the Euclidean complete solutions.