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 $\mathrm{\Delta }{\mathrm{[p}}_{n}Q({\mathrm{\Delta }}^{m-1}{y}_n)]+q_{n}Q({\mathrm{\Delta }}^{m-1}{y}_n)+r_{n}Q(y_{{\tau }_n})=0$, $n\ge n_0$, where $m$ is even and $Q(s)={\left|s\right|}^{\alpha -2}s$, $\alpha >1$ 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.