Sur une Classe d\u27Équations de Fuchs non Linéaires

For nonlinear partial differential equations, with several Fuchsian variables, we give sufficient conditions concerning the existence and uniqueness of a holomorphic solution and concerning the convergence of formal power series solutions. We reduce the proof of the theorems to the proof of the fixed-point theorem in a Banach space defined by a majorant function that is suitable to this kind of equation. We show how one can deduce the generalization of these results under Gevrey regularity hypothesis with respect to the other variables