P.Amster. M.C.Mariani, D.F.Rial Solutions of H-systems using the Green function (14K, tex) ABSTRACT. We find a solution to the mean curvature equation with Dirichlet condition using the Green representation formula. Moreover, given $H_0$ and $g_0$ for which there exists a solution to the problem, we prove that for $H$ and $g$ in appropriate neighborhoods of $H_0$ and $g_0$, there still exists a solution.