Language:   Search:   Contact
Zentralblatt MATH has released its new interface!
For an improved author identification, see the new author database of ZBMATH.

Query:
Fill in the form and click »Search«...
Format:
Display: entries per page entries
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

Highlights
Master Server

### Zentralblatt MATH Berlin [Germany]

© FIZ Karlsruhe GmbH

Zentralblatt MATH master server is maintained by the Editorial Office in Berlin, Section Mathematics and Computer Science of FIZ Karlsruhe and is updated daily.

Other Mirror Sites

Copyright © 2013 Zentralblatt MATH | European Mathematical Society | FIZ Karlsruhe | Heidelberg Academy of Sciences