zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Global behavior of the nonlinear difference equation $x_{n+1}=f(x_{n - s},x_{n - t})$. (English) Zbl 1121.39007
The authors study the length of the semi-cycle of the solutions and the global attractivity of the equilibrium of a nonlinear difference equation of the form $$ x_{n+1}=f(x_{n-s}, x_{n-t}), \quad n=0, 1, \dots.$$ They prove that the length of the semi-cycle of the solutions is less than or equal to $t$ and give sufficient conditions under which every positive solution of this equation converges to the positive equilibrium. Some known results are included and improved.

39A11Stability of difference equations (MSC2000)
Full Text: DOI
[1] Ladas, G.: Progress report on $xn+1=\alpha +\beta xn+\gamma $xn - 1A+Bxn+Cxn - 1. J. differ. Equations appl. 5, 211-215 (1995)
[2] Gibbons, C.; Kulenovic, M. R. S.; Ladas, S.: On the recursive sequence $xn+1=\alpha +\beta $xn - $1\gamma +xn$. Math. sci. Res. hot-line 4, 1-11 (2000) · Zbl 1039.39004
[3] Devault, R.; Kent, C.; Kosmala, W.: On the recursive sequence xn+1=p+xn - kxn. J. differ. Equations appl. 9, 721-730 (2003) · Zbl 1049.39026
[4] Amleh, A. M.; Georgiou, D. A.; Grove, E. A.; Ladas, G.: On the recursive sequence $xn+1=\alpha +xn - 1xn$. J. math. Anal. appl. 233, 790-798 (1999) · Zbl 0962.39004
[5] Ladas, G.: Open problems and conjecture. J. differ. Equations appl. 5, 317-321 (1995)
[6] Fan, Y.; Wang, L.; Li, W.: Global behavior of a higher order nonlinear difference equation. J. math. Anal. appl. 299, 113-126 (2004) · Zbl 1066.39008