Dirichlet problem for degenerate elliptic complex Monge-Ampere equation

We consider the Dirichlet problem $$ det ig({frac{partial^2u}{partial z_ipartial overline{z_j}}} ig)=g(z,u)quadmbox{in }Omega,, quad uig|_{ partial Omega }=varphi,, $$ where $Omega$ is a bounded open set of $mathbb{C}^{n}$ with regular boundary, $g$ and $varphi$ are sufficiently smooth functions, and $g$ is non-negative. We prove that, under additional hypotheses on $g$ and $varphi $, if $|det varphi _{ioverline{j}}-g|_{C^{s_{ast}}}$ is sufficiently small the problem has a plurisubharmonic solution.