Solutions globales de certaines équations de Fuchs non linéaires dans les espaces de Gevrey

Derrab, Faiza

doi:10.1090/S0002-9939-06-08670-9

Solutions globales de certaines équations de Fuchs non linéaires dans les espaces de Gevrey
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Proc. Amer. Math. Soc. 135 (2007), 1803-1815 Request permission

Abstract:

We consider nonlinear partial differential equations with several Fuchsian variables of type $a(t,D_{t}) u(t,x) = f(t,x,Du(t,x))$, where $a(t,D_{t})$ is a Fuchsian principal part of weight zero. We prove existence and uniqueness of a global solution to this problem in the space of holomorphic functions with respect to the Fuchsian variable $t$ and in Gevrey spaces with respect to the other variable $x$. The method of proof is based on the application of the fixed point theorem in some Banach algebras defined by majorant functions that are suitable to this kind of equation.

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