Oscillation and Nonoscillation of Asymptotically Almost Periodic Half-Linear Difference Equations

Abstract EN

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.