Abstract
New oscillation results are obtained for the second order nonlinear difference equation
Δ
(
r
n
f
(
Δ
x
n
−
1
)
)
+
g
(
n
,
x
n
)
=
0
,
and its functional form
Δ
(
r
n
f
(
Δ
x
n
−
1
)
)
+
g
(
n
,
x
τ
n
)
=
0
.
The role played by the argument
τ
n
on the oscillation of the functional equation is explored. In particular, we characterize a class of sequences
{
τ
n
}
which have a harmless effect on the oscillation of this type of equations. Some of our results generalize, improve or unify known fundamental oscillation results for several particular cases of the above equations.