Geodesic
Oscillation of third-order half-linear neutral difference equations
Mathematica Bohemica, Tome 138 (2013) no. 1, pp. 87-104

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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.
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.
DOI : 10.21136/MB.2013.143232
Classification : 39A10, 39A21
Keywords: third order neutral difference equation; oscillation; nonoscillation 
Thandapani, E.; Selvarangam, S. Oscillation of third-order half-linear neutral difference equations. Mathematica Bohemica, Tome 138 (2013) no. 1, pp. 87-104. doi: 10.21136/MB.2013.143232
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