This paper is concerned with the oscillatory behavior of first order
difference equation with general argument
![](img19.png)
where
![$\left( p(n)\right) $](img20.png)
is a sequence of nonnegative real numbers and
![$%
\left( \tau (n)\right) $](img21.png)
is a sequence of integers. Let the number
![$m$](img22.png)
be
defined by
![\begin{equation*}
m=\liminf_{n\rightarrow \infty }\dsum\limits_{j=\tau (n)}^{n-1}p(j)\left(
\frac{j-\tau (j)+1}{j-\tau (j)}\right) ^{j-\tau (j)+1}
\end{equation*}](img23.png)
. It is proved that, all solutions of Equation (
![$\star $](img24.png)
) oscillate if the
condition
m>1 is satisfied.