Global behavior and oscillation of a third order difference equation

Abstract

In this paper, we solve and study the global behavior of the admissible solutions of the difference equation x_n+1 = x_nx_{n-2 /} ax_n-1 + bx_n-2 n = 0,1,...., where a,b > 0 and the initial values x₋₂, x₋₁, x₀ are real numbers. We study also the oscillation of the admissible solutions of the aforementioned difference equation and give some illustrative examples.