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.
Citation
Faiza Derrab. Abdallah Nabaji. "Solutions holomorphes locale et globale pour un opérateur différentiel linéaire à plusieurs variables Fuchsiennes." Osaka J. Math. 42 (3) 653 - 675, September 2005.
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