Global Asymptotic Stability of a Nonautonomous Difference Equation

We study the following nonautonomous difference equation: x(n+1) = (x(n)x(n-1) + p(n))/(x(n) + x(n-1)), n = 0, 1, ..., where p(n) > 0 is a period-2 sequence and the initial values x(-1), x(0) is an element of (0, infinity). We show that the unique prime period-2 solution of the equation above is globally asymptotically stable.