New Oscillation Criteria for Half-Linear Second-Order Neutral Advanced Difference Equations

Abstract

We obtained oscillation criteria for the second-order half-linear neutral advanced difference equations of the kind ∆(α(ζ)(∆w(ζ))) + η(ζ)y(ζ + κ) = 0; ζ ≥ ζ0, where w(ζ) = y(ζ) + p(ζ)y(ζ + ξ). We provide a new oscillation condition, which significantly improves the existing ones, by providing a new axiom bound for a non-oscillatory solution. The derived oscillation constant is unimprovable in a certain nonneutral case. 2020 Mathematics Subject Classifications: 39A12, 39A13, 39A21.