Dynamics of the max-type difference equation xn+1 = max{A/xn, xn-k}
In this paper, we study the following max-type difference equation x(n+1) = max{A/x(n), x(n-k)}, n = 0, 1, ... , where A is an element of (-infinity, +infinity), k is an element of {1, 2, ... } and the initial conditions x(-k), x(-k+1), ... , x(0) is an element of (-infinity, +infinity). We show that every well-defined solution of this equation is eventually periodic with period k + 1, which confirms the truth of the conjecture proposed by Elsayed and Stevic [Nonlinear Analysis 71(2009), 910- 922].
well-defined solution periodicity max-type equation