On the nonautonomous difference equation xn+1 = An + (xpn-1 / xqn)

Abstract In this paper we study the asymptotic behavior and the periodicity of the positive solutions of the nonautonomous difference equation: x n + 1 = A n + x n - 1 p x n q , n = 0 , 1 , … , where A n is a positive bounded sequence, p , q  ∈ (0, ∞) and x −1 , x 0 are positive numbers.

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