Oscillation of Forced Nonlinear Neutral Delay Difference Equations of First Order

Abstract

Necessary and sufficient conditions are obtained for every solution of $$\Delta \left( {y_n + p_n y_n - m} \right) \pm q_n G(y_n - k) = f_n $$ to oscillate or tend to zero as n → ∞, where p n, q n and f n are sequences of real numbers such that q n ≥ 0. Different ranges for p n are considered.