On the oscillation of higher-order half-linear delay differential equations

In this paper, sufficient conditions are established for the oscillatory and asymptotic behavior of higher–order half–linear delay difference equation of the form ∆(pn(∆ (xn + qnxτn)) ) + rnx β σn = 0, n ≥ n0, where it is assumed that ∑∞ s=n0 1/p 1/α s < ∞. The main theorem improves some existing results in the literature. An example is provided to demonstrate the effectiveness of the main result.