A Maillet type theorem for first order singular nonlinear partial differential equations (Q1425472)

Summary: We shall study the first-order singular nonlinear partial differential equation of the form \(f(x,u(x),\;\partial_xu(x))=0\) with \(u(0)=0\), where \(x\in \mathbb{C}^n\) and \(f(x,u,\xi)\) is holomorphic in a neighborhood of the origin. This equation is said to be singular if \(f(0,0, \xi)\equiv 0\) for all \(\xi\in\mathbb{C}^n\). 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.