P. Amster, M. C. Mariani and D. F. Rial Existence and uniqueness of H-systems's solutions with Dirichlet conditions (13K, tex) ABSTRACT. We give conditions on the boundary data in order to obtain a solution for the problem (1) below and we prove that in certain cases the solutions are isolated. The condition $\Vert H\Vert_{\infty}\Vert g\Vert_{\infty}\le 1$ is not necessary.