In this paper, we consider a nonlinear singular second order partial differential equation of the form
\[
(
t
∂
∂
t
)
2
u
=
F
(
t
,
x
,
{
(
t
∂
∂
t
)
i
(
∂
∂
x
)
α
u
}
i
+
|
α
|
≤
2
,
i
>
2
)
\Bigl (t \frac {\partial }{\partial t} \Bigr )^2u = F \Bigl (t,x, \Bigl \{ \Bigl (t \frac {\partial }{\partial t} \Bigr )^i \Bigl (\frac {\partial }{\partial x} \Bigr )^\alpha u \Bigr \}_{i+|\alpha | \leq 2,i>2} \Bigr )
\]
in the complex domain. If
F
(
t
,
x
,
z
)
F(t,x,z)
(with
z
=
{
z
i
,
α
}
i
+
|
α
|
≤
2
,
i
>
2
z=\{z_{i,\alpha } \}_{i+|\alpha | \leq 2,i>2}
) is a holomorphic function satisfying
F
(
0
,
x
,
0
)
≡
0
F(0,x,0) \equiv 0
and
(
∂
F
/
∂
z
i
,
α
)
(
0
,
x
,
0
)
(\partial F/\partial z_{i,\alpha })(0,x,0)
≡
0
\equiv 0
(if
|
α
|
>
0
|\alpha |>0
), then this equation is called a nonlinear Fuchsian type partial differential equation in
t
t
. Under a very weak assumption, we show the uniqueness of the solution. The result is applied to the problem of analytic continuation of local holomorphic solutions of this equation.