On the oscillation of even-order half-linear functional difference equations with damping term

Abstract

We investigate the oscillatory behavior of solutions of the m th order half-linear functional difference equations with damping term of the form Δ [pn Q (Δm-1 yn) ] + qn Q (Δm-1 yn) + rn Q (y τ n) = 0, n ≥ n 0, where m is even and Q (s) = s α - 2 s, α > 1 is a fixed real number. Our main results are obtained via employing the generalized Riccati transformation. We provide two examples to illustrate the effectiveness of the proposed results. © 2014 Yaşar Bolat and Jehad Alzabut.