ABSTRACT
Abstract The aim of this paper is to present some facts about rational thirdorder difference equations and to pose open problems and conjectures about the global behavior of their solutions.
In [4] several open problems and conjectures were posed about the behavior of solutions of the equation:
xn+1 = α+ βxn + γxn−1 + δxn−2
A+Bxn +Dxn−2 , n = 0, 1, ... (1)
with nonnegative parameters and nonnegative initial conditions. One can see that Eq. (1) possesses period-two solutions if and only if
γ = β + δ +A . (2)
The following open problem was posed in [4].
