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

MSC:

39A11 Stability of difference equations (MSC2000)
39B05 General theory of functional equations and inequalities
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