Oscillation and nonoscillation of nonlinear neutral delay difference equations

Abstract

In this paper, the authors establish some sufficient conditions for oscillation and nonoscillation of the second order nonlinear neutral delay difference equation

$$ \Delta^2 (x_n-p_nx_{n-k}) + q_nf(x_{n-\ell}) = 0, ~~n \ge n_0 $$

where $ \{p_n\} $ and $ \{q_n\} $ are non-negative sequences with $ 0$