Maillet type theorem for nonlinear partial differential equations and Newton polygons

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Abstract

It is known that the formal solution to an equation of non-Kowalevski type is divergent in general. To this divergent solution it is important to evaluate the rate of divergence or the Gevrey order, and such a result is often called a Maillet type theorem. In this paper the Maillet type theorem is proved for divergent solutions to singular partial differential equations of non-Kowalevski type, and it is shown that the Gevrey order is characterized by a Newton polygon associated with an equation. In order to prove our results the majorant method is effectively employed.

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