COMPARISON THEOREMS ON THE OSCILLATION OF A CLASS OF NEUTRAL DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLES

Abstract. In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form ∇α [x (t) − r (t)x (t − κ)] + p (t)x (t − τ) − q (t)x (t − σ) = 0, t ≥ t0, where t0 ∈ R, t varies in the real interval [t0,∞), α> 0, κ, τ, σ ≥ 0, r ∈ C `[t0 − α,∞),R+´, p, q ∈ C `[t0,∞),R+ ´ and ∇αx (t) = x (t) − x (t − α) for t ≥ t0. 1