Solutions of H-systems using the Green function P. Amster M. C. Mariani D.F. Rial 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. 1 Introduction We consider the Dirichlet problem in a bounded smooth domain Ω ⊂ R 2 for a vector function X : Ω −→ R 3 satisfying the prescribed mean curvature equation (1)    ΔX =2H (u,v,X )X u ∧ X v in Ω X = g on ∂ Ω where X u and X v are the partial derivatives of X , ∧ denotes the exterior product in R 3 . We’ll assume that H : Ω × R 3 −→ R is continuous and that g is smooth. Without loss of generality, we may extend g to a harmonic function in C 1 ( Ω). Problem (1) and the general Plateau problem have been studied by variational methods for constant H and H = H (X ) in [BC], [H], [LDM], [S], [W], among other authors. Topological methods are applied for the case H = H (u, v ) in [AMR]. Received by the editors November 1999. Communicated by J. Mawhin. Bull. Belg. Math. Soc. 7 (2000), 487–492