Oscillation of second order nonlinear delay difference equations

Bull. Korean Math. Soc. 2003 Vol. 40, No. 3, 489-501 Published online September 1, 2003

S. H. Saker Mansoura University

Abstract : 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.