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On a class of nonlinear Fuchsian equations. (Sur une classe d’équations de Fuchs non linéaires.) (French) Zbl 0964.35008
Summary: 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.

35A07 Local existence and uniqueness theorems (PDE) (MSC2000)
35A20 Analyticity in context of PDEs
35A10 Cauchy-Kovalevskaya theorems
35C10 Series solutions to PDEs