We consider nonlinear singular partial differential equations of the form (
tDt−ρ(
x))
u=
ta(
x)+
G2(
x) (
t,
tDtu,
u,
D1u, ..,
Dnu).
It has been proved by Gérard and Tahara that there exists a unique holomorphic solution with
u(0,
x)≡0 if the characteristic exponent ρ(
x) avoids positive integral values. In the present paper we consider what happens if ρ(
x) takes a positive integral value at
x=0. Genetically, the solution
u(
t,
x) is singular along the analytic set {
t=0, ρ(
x)∈
N*},
N*={1, 2, ..}, and we investigate how far it can be analytically continued.
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