Global stability of a rational difference equation

Abstract

We consider the higher-order nonlinear difference equation x n 1 p qx n−k / 1 x n rx n−k , n 0, 1, . . . with the parameters, and the initial conditions x −k , . . . , x 0 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 particular, our results solve the open problem introduced by Kulenović and Ladas in their monograph see Kulenović and Ladas, 2002 .

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