Applications of Langenhop inequality to difference equations: Lower bounds and oscillation.

Zafer, Ağacık

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Some new criteria for the oscillation of third order nonlinear neutral difference equations of the form $Δ (a_{n} {(Δ^{2} (x_{n} + b_{n} x_{n - δ}))}^{α}) + q_{n} x_{n + 1 - τ}^{α} = 0$ and $Δ (a_{n} {(Δ^{2} (x_{n} - b_{n} x_{n - δ}))}^{α}) + q_{n} x_{n + 1 - τ}^{α} = 0$ are established. Some examples are presented to illustrate the main results.