Oscillatory behavior of third order nonlinear difference equation with mixed neutral terms

In this paper, we obtain some new sufficient conditions for the oscillation of all solutions of the third order nonlinear neutral difference equation of the form \begin{equation*} \Delta^3 \left(x_n+b_n x_{n-\tau_{1}}+c_n x_{n+\tau_{2}}\right)^{\alpha} = q_n x_{n-\sigma_1}^{\beta}+p_n x_{n+\sigma_2}^{\gamma}, \quad n\geq n_0, \end{equation*} where $\alpha,$ $\beta,$ and $\gamma$ are the ratios of odd positive integers. Examples are given to illustrate the main results

Oscillation of third-order half-linear neutral difference equations

summary:Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form \begin {equation*} \Delta (a_n(\Delta ^2(x_n+b_{n}x_{n-\delta }))^\alpha )+q_{n}x^{\alpha }_{n+1-\tau }=0 \end {equation*} and \begin {equation*} \Delta (a_n(\Delta ^2(x_n-b_nx_{n-\delta }))^\alpha )+q_nx^{\alpha }_{n+1-\tau }=0 \end {equation*} are established. Some examples are presented to illustrate the main results

Oscillation criteria for even order neutral difference equations

In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form Δm(xn + axn-τ1 + bxn+τ2 ) + pnxα n-σ1 + qnxβ n+σ2 = 0, n ≥ n0 > 0, where m ≥ 2 is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results. © 2019 Wydawnictwa AGH, Krakow

Oscillation criteria for even order neutral difference equations

In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form [formula] where m ≥ 2 is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results

Oscillation of nonlinear third order perturbed functional difference equations

This paper deals with oscillatory and asymptotic behavior of all solutions of perturbed nonlinear third order functional difference equatio

Oscillation criteria for even order neutral difference equations

In this paper, we present some new sufficient conditions for oscillation of even order nonlinear neutral difference equation of the form Δm(xn + axn-τ1 + bxn+τ2 ) + pnxα n-σ1 + qnxβ n+σ2 = 0, n ≥ n0 > 0, where m ≥ 2 is an even integer, using arithmetic-geometric mean inequality. Examples are provided to illustrate the main results. © 2019 Wydawnictwa AGH, Krakow

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