Regularity for "general form" Monge-Ampère equation

Question

I'm looking for conditions under which the following general form Monge-Ampère equation has a $\mathcal{C}^2(\mathbb{R}^2)$-solution:

$$ det(D^2u-A(x,u))=B(x,u).$$

I'm not sure whether such conditions exist at all as I'm looking for a solution on an unbounded domain (which matters, right?).

The three cases I'm interested in are

1. $B=0$
2. $B\geq0$
3. $B\geq c>0$.

For this equation I could only find results on a bounded domain. Furthermore, to my maybe flawed understanding the Evans-Krylov can only apply in case 3. Also some results only apply to the case where $B=B(x,\nabla u)$...

Any reference is welcome, too!

Thanks in advance and sorry for my lack of PDE-knowledge...