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.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
7
号
3
ページ
423 - 448
発行年
2000
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathematical Reviews Number
MR1792735
Mathmatical Subject Classification
35A07(MSC1991)
35A20(MSC1991)
35A10(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
Sur une Classe d'Équations de Fuchs non Linéaires
jms070304.pdf
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