The Stability of High Order Max-Type Difference Equation

On the Global Attractivity of a Max-Type Difference Equation

On a max-type and a min-type difference equation

This note shows that every positive solution to the following third order non–autonomous max-type difference equation

Eventually Periodic Solutions of a Max-Type Difference Equation

We study the following max-type difference equation xn = max{A(n)/x(n-r), x(n-k)}, n = 1,2,…, where {A(n)} n=1 (+∞) is a periodic sequence with period p and k, r ∈ {1,2,…} with gcd(k, r) = 1 and k ≠ r, and the initial conditions x(1-d), x(2-d),…, x 0 are real numbers with d = max{r, k}. We show that if p = 1 (or p ≥ 2 and k is odd), then every well-defined solution of this equation is eventuall...

Research Article On a Max-Type Difference Equation

Global Behavior of the Max-Type Difference Equation xn+1=max{1/xn,An/xn-1}

and Applied Analysis 3 Lemma 2.5. Let {xn}n −1 be a positive solution of 1.1 and limn→∞Pn S. Then S lim supn→∞xn. Proof. Since Pn is a subsequence of xn, it follows that S ≤ lim sup n→∞ xn. 2.6 On the other hand, by xn 1 ≤ Pn for all n ≥ 1, we obtain lim sup n→∞ xn ≤ lim sup n→∞ Pn S. 2.7 The proof is complete. Remark 2.6. Let {xn}n −1 be a positive solution of 1.1 . By Lemma 2.2, we see that i...