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Zbl 1095.39010
Stević, Stevo
On positive solutions of a ($k+1$)th order difference equation.
(English)
[J] Appl. Math. Lett. 19, No. 5, 427-431 (2006). ISSN 0893-9659

The author proves that the following difference equation $$x_{n+1}=\frac{x_{n-k}}{1+x_{n}+\cdots + x_{n-k+1}},\quad n=0, 1, \cdots,$$ where $k\in {\Bbb N}$, has a positive solution which converges to zero. This result solves Open Problem 11.4.10 (a) of {\it M. R. S. Kulenović} and {\it G. Ladas} [Dynamics of second order rational difference equations. With open problems and conjectures. (Boca Raton, FL: Chapman and Hall/CRC) (2002; Zbl 0981.39011)].
[Zhiming Guo (Guangzhou)]
MSC 2000:
*39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: Rational difference equations; positive solutions; convergence to zero

Citations: Zbl 0981.39011

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