Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1153.39015
Hu, Lin-Xia; Li, Wan-Tong; Stević, Stevo
Global asymptotic stability of a second order rational difference equation. (English)
[J] J. Difference Equ. Appl. 14, No. 8, 779-797 (2008). ISSN 1023-6198

This paper studies the properties of solutions of the rational difference equation $$ x_{n+1}=\frac{\beta x_n+\gamma x_{n-1}}{A+Bx_n+Cx_{n-1}}, \quad n\in{\mathbb N}_0, \tag{$*$} $$ where $\beta,\gamma,A,B,C\in(0,\infty)$ and the initial conditions $x_{-1},x_0\in[0,\infty)$ are not both zero. \par The main result answers positively the open problem posed by {\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 \& Hall/CRC (2002; Zbl 0981.39011), Conjecture 9.5.5], i.e., the positive equilibrium point of equation ($*$) is globally asymptotically stable. Furthermore, the authors prove the boundedness of every nonnegative solution and provide a detailed analysis of the invariant intervals and semicycles.
[Roman Šimon Hilscher (Brno)]

MSC 2000:: *39A11 Stability of difference equations
39A20 Generalized difference equations

Keywords: bounded solution; invariant interval; semicycle; global attractor; asymptotic stability; rational difference equation; positive equilibrium; nonnegative solution

Citations: Zbl 0981.39011

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]