## International Journal of Differential Equations

### 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 $Q(s)={|s|}^{\alpha -2}s$, $\alpha >1$ 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.

#### Article information

Source
Int. J. Differ. Equ., Volume 2014 (2014), Article ID 791631, 6 pages.

Dates
Received: 6 February 2014
Revised: 2 May 2014
Accepted: 6 May 2014
First available in Project Euclid: 20 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.ijde/1484881401

Digital Object Identifier
doi:10.1155/2014/791631

Mathematical Reviews number (MathSciNet)
MR3214492

Zentralblatt MATH identifier
1291.39032

#### Citation

Bolat, Yaşar; Alzabut, Jehad. On the Oscillation of Even-Order Half-Linear Functional Difference Equations with Damping Term. Int. J. Differ. Equ. 2014 (2014), Article ID 791631, 6 pages. doi:10.1155/2014/791631. https://projecteuclid.org/euclid.ijde/1484881401

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