Sur une Classe d'Équations de Fuchs non Linéaires

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

Pongérard, Patrice
Sur une Classe d'Équations de Fuchs non Linéaires
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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.

Mathematics Subject Classification (1991): Primary 35A07; Secondary 35A20, 35A10
Mathematical Reviews Number: MR1792735

Received: 1999-07-01