A necessary and sufficient condition is given for the oscillation of all solutions of the differential equation
\[
x
(
n
)
+
P
(
t
,
x
,
x
′
,
⋯
,
x
(
n
−
1
)
)
=
Q
(
t
)
{x^{(n)}} + P(t,x,x’, \cdots ,{x^{(n - 1)}}) = Q(t)
\]
where
x
1
P
(
t
,
x
1
,
x
2
,
⋯
,
x
n
)
>
0
{x_1}P(t,{x_1},{x_2}, \cdots ,{x_n}) > 0
for every
x
1
≠
0
{x_1} \ne 0
, and Q is a continuous periodic function. This result answers a question recently raised by J. S. W. Wong. It is also shown that a well-known sufficient condition for the existence of at least one nonoscillatory solution of the unperturbed equation guarantees, for a large class of equations, the nonexistence of bounded oscillatory solutions.