# 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)
Invariants and oscillation for systems of two nonlinear difference equations. (English) Zbl 1003.39007
This paper is devoted to the invariants, boundedness and persistence of solutions for systems of two nonlinear difference equations of order $k+1$ of a special rational form. The authors also study the oscillatory behavior of the solutions of a system of two difference equations of rational form $$x_{n+1}= {1+y_n\over y_{n-1}},\ y_{n+1}= {1+x_n\over x_{n-1}}, n=0,1,\dots.$$

##### MSC:
 39A11 Stability of difference equations (MSC2000) 39B05 General theory of functional equations
Full Text:
##### References:
 [1] Grove, E. A.; Janowski, E. J.; Kent, C. M.; Ladas, G.: On a rational recursive sequence. Commun. appl. Nonlinear anal. 1, No. 3, 61-72 (1994) · Zbl 0856.39011 [2] E.A. Grove, C. Kent, G. Ladas, Lyness equations with variable coefficients, in: Proceedings of the Second International Conference on Difference Equations and Applications, Gordon and Breach Science Publishers, 1997, August 7--11, 1995, Veszprem, Hungary. · Zbl 0890.39014 [3] Ladas, G.: Invariants for generalized lyness equations. Journal of difference equations and applications 1, 209-214 (1995) · Zbl 0858.39002 [4] Kocic, V. L.; Ladas, G.: Global behavior of nonlinear difference equations of higher order with applications. (1993) · Zbl 0787.39001 [5] Papaschinopoulos, G.; Schinas, C.: On the behavior of the solutions of a system of two nonlinear difference equations. Communications on applied nonlinear analysis 5, No. 2, 47-59 (1998) · Zbl 1110.39301 [6] Papaschinopoulos, G.; Schinas, C.: Invariants for systems of two nonlinear difference equations. Differential equations and dynamical systems 7, No. 2, 181-196 (1999) · Zbl 0978.39014 [7] Schinas, C.: Invariants for difference equations and systems of difference equations of rational form. Journal of mathematical analysis and applications 216, 164-179 (1997) · Zbl 0889.39006 [8] Schinas, C.: Invariants for some difference equations. Journal of mathematical analysis and applications 212, 281-291 (1997) · Zbl 0879.39001