We analyse half-linear difference equations with asymptotically almost periodic coefficients. Using the adapted Riccati transformation, we prove that these equations are conditionally oscillatory. We explicitly find a constant, determined by the coefficients of a given equation, which is the borderline between the oscillation and the nonoscillation of the equation. We also mention corollaries of our result with several examples.
"Oscillation and Nonoscillation of Asymptotically Almost Periodic Half-Linear Difference Equations." Abstr. Appl. Anal. 2013 1 - 12, 2013. https://doi.org/10.1155/2013/432936