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.
Citation
Akira SHIRAI. "Maillet type theorem for nonlinear partial differential equations and Newton polygons." J. Math. Soc. Japan 53 (3) 565 - 587, July, 2001. https://doi.org/10.2969/jmsj/05330565
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