Consider the rational difference equation
where are positive real numbers, is a positive integer, and the initial conditions are nonnegative real numbers. The authors solve an open problem posed by M. R. S. Kulenović and G. Ladas [Dynamics of second order rational difference equations, Chapman & Hall / CRC, Boca Raton, FL (2002; Zbl 0981.39011), p. 129]. They prove the following
Theorem: (a) If then the zero equilibrium of Eq. () is globally asymptotically stable. (b) If then the positive equilibrium of Eq. () is globally asymptotically stable.
The boundedness, periodic character, invariant intervals of all nonnegative solutions of () are investigated.