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

Pongérard, Patrice

J. Math. Sci., Tokyo 7, No. 3, 423-448 (2000).

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.

MSC:

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

Keywords:

several Fuchsian variables; existence and uniqueness of a holomorphic solution; convergence of formal power series solutions; Gevrey regularity hypothesis