zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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 recursive sequence x n+1 =AΠ i=l k x n-2i-1 B+CΠ i=l k-1 x n-2i . (English) Zbl 1152.39308

Summary: The aim of this work is to investigate the global stability, periodic nature, oscillation and the boundedness of solutions of the difference equation

x n+1 =AΠ i=l k x n-2i-1 B+CΠ i=l k-1 x n-2i ,n=0,1,...

where A,B,C are nonnegative real numbers and l,k are nonnegative integers, l<k. We discuss the existence of unbounded solutions under certain conditions when l=0.

MSC:
39A11Stability of difference equations (MSC2000)
References:
[1]Ladas, G.: Open problems and conjectures, J. difference equ. Appl., 339-341 (1996)
[2]Li, X.; Zhu, D.: Global asymptotic stability for two recursive difference equations, Appl. math. Comput. 150, No. 2, 481-492 (2004) · Zbl 1044.39006 · doi:10.1016/S0096-3003(03)00286-8
[3]Nesemann, T.: Positive solution difference equations: some results and applications, Nonlinear anal. 47, 4707-4717 (2001) · Zbl 1042.39510 · doi:10.1016/S0362-546X(01)00583-1
[4]Stević, S.: Global stability and asymptotics of some classes of rational difference equations, J. math. Appl. 316, 60-68 (2006) · Zbl 1090.39009 · doi:10.1016/j.jmaa.2005.04.077
[5]Yang, X.: On the global asymptotic stability of the difference equation xn=xn-1xn-2+xn-3+axn-1+xn-2xn-3+a, Appl. math. Comput. 171, 857-861 (2005) · Zbl 1093.39012 · doi:10.1016/j.amc.2005.01.093
[6]Hamza, A. E.; Khalaf-Allah, R.: Global behavior of a higher order difference equation, J. math. Stat. 3, No. 1, 17-20 (2007) · Zbl 1186.39024 · doi:10.3844/jmssp.2007.17.20
[7]Kocic, V. L.; Ladas, G.: Global behavior of nonlinear difference equations of higher order with applications, (1993)
[8]Kulenovic, M. R. S.; Ladas, G.: Dynamics of second order rational difference equations with open problems and conjectures, (2002)