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Title: On the dynamics of a rational difference equation
Authors: Saleh, Mohammad
Keywords: Difference equations;Integro-differential equations - Asymptotic theory;Equilibrium point;Semi-cycles
Issue Date: 2017
Abstract: In this paper, we will investigate the dynamics of a nonlinear rational difference equation of a higher order. Our concentration is on invariant intervals, periodic character, the character of semi-cycles and global asymptotic stability of all positive solutions of xn+1 = α + βxn + γ xn−k Bxn + Cxn−k , n = 0, 1, . . . It is worth to mention that our results solve partially some of the open problems proposed by Kulenvic and Ladas in their monographs [17], [18].
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