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Sufficient conditions for oscillatory behaviour of a first order neutral difference equation with oscillating coefficients. (English) Zbl 1224.39018

Summary: We obtain sufficient conditions so that every solution of neutral functional difference equation

Δ(y n -p n y τ(n) )+q n G(y σ(n) )=f n

oscillates or tends to zero as n. Here, Δ is the forward difference operator given by Δx n =x n+1 -x n , and p n , q n , f n are the terms of oscillating infinite sequences; {τ n } and {σ n } are non-decreasing sequences, which are less than n and approaches as n approaches . This paper generalizes and improves some recent results.

MSC:
39A21Oscillation theory (difference equations)
39A10Additive difference equations
39A12Discrete version of topics in analysis
39A22Growth, boundedness, comparison of solutions (difference equations)
34K40Neutral functional-differential equations
34K11Oscillation theory of functional-differential equations