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Zbl 1158.39301
Saleh, M.; Abu-Baha, S.
Dynamics of a higher order rational difference equation. (English)
[J] Appl. Math. Comput. 181, No. 1, 84-102 (2006). ISSN 0096-3003

Summary: We will investigate a nonlinear rational difference equation of higher order. Our concentration is on invariant intervals, periodic character, the character of semicycles and global asymptotic stability of all positive solutions of $$x_{n+1}=\frac{\beta x_n+\gamma x_{n-k}}{Bx_n+Cx_{n-k}}\,,\quad n=0,1,\dots\,.$$ It is worth to mention that our results solve the open problem proposed by {\it H. L. S. Kulenvić} and {\it G. Ladas} in their monograph [Dynamics of second order rational difference equations: with open problems and conjectures, Chapman \& Hall/CRC, Boca Raton (2002; Zbl 0981.39011)].

MSC 2000:: *39A20 Generalized difference equations

Keywords: recursive sequence; global asymptotic stability

Citations: Zbl 0981.39011

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