Osaka Journal of Mathematics

Solutions holomorphes locale et globale pour un opérateur différentiel linéaire à plusieurs variables Fuchsiennes

Faiza Derrab and Abdallah Nabaji

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Abstract

We consider linear partial differential equations with several Fuchsian variables in the sense of M.S. Baouendi and C. Goulaouic [1]. For a holomorphic Fuchsian operator with holomorphic Fuchsian principal part, we prove existence and uniqueness of a holomorphic local solution. Our theorem generalizes the results of ([3, 1, 11]), precises the one of [4] and reduces the proof of their theorems to the proof of the fixed-point theorem. For a holomorphic Fuchsian operator with constant Fuchsian principal part, we establish the existence and uniqueness of a holomorphic global solution. Our aim is to simplify its proof. The methods of proof are based on the application of the fixed-point theorem in some Banach spaces defined by majorant functions that are suitable to this kind of equations.

Article information

Source
Osaka J. Math., Volume 42, Number 3 (2005), 653-675.

Dates
First available in Project Euclid: 21 July 2006

Permanent link to this document
https://projecteuclid.org/euclid.ojm/1153494507

Zentralblatt MATH identifier
1330.35007

Citation

Derrab, Faiza; Nabaji, Abdallah. Solutions holomorphes locale et globale pour un opérateur différentiel linéaire à plusieurs variables Fuchsiennes. Osaka J. Math. 42 (2005), no. 3, 653--675. https://projecteuclid.org/euclid.ojm/1153494507


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