On the oscillation of higher-order half-linear delay difference 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 Delta(p(n)(Delta(m-1)(x(n) + q(n)x(tau n)))(alpha)) + r(n)x(sigma n)(beta) = 0, n >= n(0), where it is assumed that Sigma(infinity)(s=n0) 1/(s1/alpha)(p) < infinity. The main theorem improves some existing results in the literature. An example is provided to demonstrate the effectiveness of the main result.