On the Recursive Sequence xn 1 A x p n − 1 / x q n
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On the Recursive Sequence
The paper considers the boundedness character of positive solutions of the difference equation xn+1 = A+ x n /x n−1, n ∈ N0, where A, p, and r are positive real numbers. It is shown that (a) If p2 ≥ 4r > 4, or p ≥ 1 + r, r ≤ 1, then this equation has positive unbounded solutions; (b) if p2 < 4r, or 2 √ r ≤ p < 1+ r, r ∈ (0,1), then all positive solutions of the equation are bounded. Also, an an...
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