Oscillation criteria for higher-order half-linear delay difference equations involving generalized difference operator

Abstract

In this paper, oscillation criteria are obtained for higher-order half-linear delay difference equations involving generalized difference operator of the form [Equation presented here] where Δb is defined by Δbyn = yn+1 - byn, b ∈ R - {0}, p: N → R+, α, β are the ratio of odd positive integers with β ≤ α; m, n, n0, σ are non-negative integers, q: N → R. The cases of b negative and positive and qn ≥ 0, which has important role for oscillation of this equation, are considered. Also we provide some examples to illustrate our main results.