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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 $$x_{n+1}= {1+y_n\over y_{n-1}},\ y_{n+1}= {1+x_n\over x_{n-1}}, n=0,1,\dots.$$

39A11Stability of difference equations (MSC2000)
39B05General theory of functional equations
Full Text: DOI
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[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