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We consider the higher-order nonlinear difference equation xn 1 p qxn−k / 1 xn rxn−k , n 0, 1, . . . with the parameters, and the initial conditions x−k, . . . , x0 are nonnegative real numbers. We investigate the periodic character, invariant intervals, and the global asymptotic stability of all positive solutions of the above-mentioned equation. In(More)
In this paper, we investigate the global attractivity of negative solutions of the nonlinear difference equation xn+1 = 1− xn−k A + xn , n = 0, 1, . . . , where A ∈ (−∞, 0), k is a positive integer and initial conditions x−k, · · · , x0 are arbitrary real numbers. We show that the unique negative equilibrium of abovementioned equation is a global attractor(More)
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