RT info:eu-repo/semantics/article
T1 Maillet type theorem for nonlinear totally characteristic partial differential equations
A1 Lastra Sedano, Alberto
A1 Tahara , Hidetoshi
K1 Matemáticas
K1 Mathematics
AB The paper discusses a holomorphic nonlinear singular partial differential equation (t∂t)mu=F(t,x,{(t∂t)j∂αxu}j+α≤m,j<m)(t∂t)mu=F(t,x,{(t∂t)j∂xαu}j+α≤m,j<m) under the assumption that the equation is of nonlinear totally characteristic type. By using the Newton polygon at x=0x=0, the notion of the irregularity at x=0x=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.
PB Springer
SN 0025-5831
YR 2019
FD 2019-07-05
LK http://hdl.handle.net/10017/41535
UL http://hdl.handle.net/10017/41535
LA eng
NO Ministerio de Economía y Competitividad
DS MINDS@UW
RD 29-nov-2023