  We study the Monge-Ampere equation with some power nonlinear term. A solution
u is called to be Euclidean complete if it is an entire solution defined over
the whole R^n or its graph is a large hypersurface satisfying the large
condition on boundary \partial\Omega in case \Omega\not=R^n. In this paper, we
will give various sharp conditions on p and \Omega classifying the Euclidean
complete solution. Our results clarify and extend largely the existence theorem
of Cirstea-Trombetti (Calc. Var., 31, 2008, 167-186) for bounded convex domain
and p>n.
