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 attractivity in a higher order nonlinear difference equation. (English) Zbl 1004.39010
The nonlinear rational difference equations are of paramount importance in their own right, and furthermore for the development of the basic theory of the global behavior of nonlinear difference equations. The authors study the global attractivity of the rational recursive sequence $$X_{n+1}=(a-bX_{n})/(c-X_{n-k}), \quad n=0,1,\dots, \tag 1$$ where $a >$ or equal $0, c>b>0$ are real numbers and $k>$ or equal 1 is an integer, and the initial conditions $X_{-k} ,X_{-k+1},\dots ,X_{-1}$ and $X_{0}$ are arbitrary. They prove that the positive equilibrium of equation (1) is a global attractor with a basin that depends on certain conditions of the coefficients. I think that the authors must be aware of relevant published papers on the same topic, for example {\it W. A. Kosmala, M. R. S. Kulenovic, G. Ladas} and {\it C. T. Teixeira} [J. Math. Anal. Appl. 251, No. 2, 571-586 (2000; Zbl 0967.39004)].

39A11Stability of difference equations (MSC2000)
39B05General theory of functional equations
Full Text: EMIS EuDML