More results on the trichotomy character of a second-order rational difference equation with period-two coefficients

摘要

We extend the known results of the non-autonomous difference equation to the situation where (i) the parameters β_n, γ_n, A_n and B_n are period-two sequences of non-negative real numbers with γ_n not identically zero and A_n+B_n ≠ 0 and (ii) the initial conditions x_(-1) and x_0 are such that x_(-1), x_0 ∈ (0, ∞)and x_(-1) + x_0 ∈ (0, ∞).