#### S. Selvarangam, S. Geetha, E. Thandapani, Oscillation and asymptotic behavior of third order nonlinear neutral difference equations with mixed type, Vol. 2017 (2017), Article ID 2, pp. 1-17

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DOI: 10.23952/jnfa.2017.2

Received July 27, 2016; Accepted November 22, 2016

Abstract. This paper concerned with the oscillatory and asymptotic behavior of third order difference equation with mixed type neutral term $\Delta\left(a_{n}\Delta^{2}\left(x_{n}+b_{n}x_{n-\tau_{1}}+c_{n}x_{n+\tau_{2}}\right)^{\alpha}\right)+q_{n}x_{n-\sigma_{1}}^{\beta} +p_{n}x_{n+\sigma_{2}}^{\gamma}=0.$ Using arithmetic-geometric mean inequality, we obtained oscillation criteria which generalize and extend some of the known results. Examples are also provided to illustrate the main results.