Oscillation criteria for higher-order neutral type difference equations

Abstract

In this paper, oscillation criteria are obtained for higher-order neutral-type nonlinear delay difference equations of the form ∆(rn(∆k−1 (yn + pnyτn )) + qnf(yσn ) = 0, n ≥ n0, (0.1) where rn, pn, qn ∈ [n0, ∞), rn > 0, qn > 0; 0 ≤ pn ≤ p0 < ∞; limn→∞ τn = ∞, limn→∞ σn = ∞; σn ≤ n, σn is nondecreasing; ∆τn ≥ τ0 > 0; τσ = στ ;f(u) u ≥ m > 0 for u ̸= 0. Moreover, we provide some examples to illustrate our main results.