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Global behavior of the nonlinear difference equation $x_{n+1}=f(x_{n - s},x_{n - t})$. (English) Zbl 1121.39007
The authors study the length of the semi-cycle of the solutions and the global attractivity of the equilibrium of a nonlinear difference equation of the form $$x_{n+1}=f(x_{n-s}, x_{n-t}), \quad n=0, 1, \dots.$$ They prove that the length of the semi-cycle of the solutions is less than or equal to $t$ and give sufficient conditions under which every positive solution of this equation converges to the positive equilibrium. Some known results are included and improved.

##### MSC:
 39A11 Stability of difference equations (MSC2000)
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##### References:
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