2003 Volume 39 Issue 2 Pages 275-296
We shall study the first order singular nonlinear partial differential equation of the form f(x, u(x), ∂xu(x))=0 with u(0)=0, where x∈Cn and f(x, u, ξ) is holomorphic in a neighborhood of the origin. This equation is said to be singular if f(0, 0, ξ)≡0 for all ξ∈Cn. The purpose of this paper is to study the Maillet type theorem which means to determine the Gevrey order of a formal power series solution which may diverge.
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