Volume 35 • Number 3 • 2012   • Oscillation of a Certain Class of Third Order Nonlinear Difference Equations S. H. Saker Abstract. In this paper, we are concerned with oscillation of the nonlinear difference equation $\Delta (c_{n}\left[ \Delta (d_{n}\Delta x_{n})\right] ^{\gamma })+q_{n}f(x_{g(n)})=0,\ n\geq n_{0},$ where $\gamma >0$ is the quotient of odd positive integers, $c_{n}$, $d_{n}$ and $q_{n}$ are positive sequences of real numbers, $g(n)$ is a sequence of nonnegative integers and $f\in C(\mathbf{R,R)}$ such that $uf(u)>0$ for $% u\neq 0.$ We establish some new sufficient conditions for oscillation by employing the Riccati substitution and the analysis of the associated Riccati difference inequality. Our results extend and improve some previously obtained ones. Some examples are considered to illustrate the main results. 2010 Mathematics Subject Classification: 34K11, 39A10. Full text: PDF