In this note we consider the stationary Kirchhoff equation
\[
{
−
M
(
‖
u
‖
2
)
Δ
u
=
f
(
x
,
u
)
a
m
p
;
in
Ω
,
u
=
0
a
m
p
;
on
∂
Ω
,
\left \{ \begin {array}{ll} -M(\| u\|^2) \Delta u = f(x,u) & \hbox {in }\Omega ,\\ \ \ u=0 & \hbox {on }\partial \Omega , \end {array} \right .
\]
where
M
M
is a continuous positive function and
‖
⋅
‖
\| \cdot \|
is the standard norm in
H
0
1
(
Ω
)
H_0^1(\Omega )
. We show that the equation does not enjoy the usual comparison principles (both weak or strong) nor the sub and supersolutions method.