Bulletin of the
Korean Mathematical Society BKMS

In this paper we shall consider the nonlinear delay difference
equation
\[
\Delta (p_{n}\Delta x_{n})+q_{n}f(x_{n-\sigma })=0,\qquad n=0,1,2,\ldots%
\]
when $\sum\limits_{n=n_{0}}^{\infty }\frac{1}{p_{n}}<\infty $. We
will establish some sufficient conditions which guarantee that
every solution is oscillatory or converges to zero.

Keywords: oscillation, nonlinear delay difference equations

MSC numbers: 39A10