Abstract
In this paper, we will investigate a nonlinear rational difference equation of higher order. Our concentration is on invariant intervals, periodic character, the character of global asymptotic stability of all positive solutions of It is worth to mention that our results solve the open problem proposed by Kulenvic and Ladas in their monograph (M.R.S. Kulenović and G. Ladas, Dynamics of Second Order Rational Difference Equations with Open Problems and Conjectures, Chapman & Hall/CRC, Boca Raton, 2002).
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