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• W2896048798 abstract "The paper discusses a holomorphic nonlinear singular partial differential equation $$(t partial _t)^mu=F(t,x,{(t partial _t)^j partial _x^{alpha }u }_{j+alpha le m, j<m})$$ under the assumption that the equation is of nonlinear totally characteristic type. By using the Newton polygon at $$x=0$$ , the notion of the irregularity at $$x=0$$ of the equation is defined. In the case where the irregularity is greater than one, it is proved that every formal power series solution belongs to a suitable formal Gevrey class. The precise bound of the order of the formal Gevrey class is given, and the optimality of this bound is also proved in a generic case." @default.
• W2896048798 created "2018-10-26" @default.
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• W2896048798 date "2019-07-05" @default.
• W2896048798 modified "2023-10-13" @default.
• W2896048798 title "Maillet type theorem for nonlinear totally characteristic partial differential equations" @default.
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• W2896048798 doi "https://doi.org/10.1007/s00208-019-01864-x" @default.
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