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Titlebook: Singular Nonlinear Partial Differential Equations; Raymond Gérard,Hidetoshi Tahara Book 1996 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

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,Maillet’s type theorems for non linear singular partial differential equations without linear part,d explicitly. We showed also in [19] (see also section 6.4 of chapter 6) that for some particular equations the number . (û) is the exact formal Gevrey index of û. The main assumption in chapter 6 was that the equation (6.3.1) has a linear part.
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Operators with regular singularities: Several variables case, studying formal linear equations and then we are looking at the analytic case. This means that we are giving conditions under which the formal power series solutions that we obtained in part A are convergent.
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Local study of differential equations of the form , = , near , = 0,olomorphic near the origin of ℂ.. In particular, we are looking for a normal form of (4.0.1). We have a transformation . which is reducing (4.0.1) to a normal form and this transformation is given as a solution of a partial differential equation of the form . where . is holomorphic near the origin o
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