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)
On the rational recursive sequence $x_{n+1}=\frac {ax_{n-1}}{b+cx_nx_{n-1}}$. (English) Zbl 1212.39008
Consider the difference equation $$ x_{n+1}=\frac {ax_{n-1}}{b+cx_nx_{n-1}},\quad n=0,1,\dots, $$ with $a,b,c$ positive real numbers, and nonnegative initial conditions $(x_{-1},x_0)$. By a change of variables, it is reduced to $$ y_{n+1}=\frac {y_{n-1}}{p+y_ny_{n-1}},\quad n=0,1,\dots, \tag 1 $$ where $p=b/a$, $x_n=(a/c)^{1/2}y_n$. Since this equation is semiconjugate to a Möbius transformation [cf. {\it {A. Andruch-Sobiło}}, {\it {M. Migda}}, Opusc. Math. 26, No. 3 387--394 (2006; Zbl 1131.39003)], a formula for the solutions is available in terms of the parameter $p$ and the initial data. The authors use this formula to prove that every positive solution of (1) converges to zero if $p\geq 1$, and converges to a periodic solution of period two if $0<p<1$. [For recent results concerning the same equation, see {\it {H. Sedaghat}}, J. Difference Equ. Appl. 15, No. 3, 215--224 (2009; Zbl 1169.39006)].

39A20Generalized difference equations
39A22Growth, boundedness, comparison of solutions (difference equations)