Global attractivity of a higher order nonlinear difference equation. (English) Zbl 1081.39005

The authors investigate the global attractivity of a positive equlibrium of equations of the form \(y_{n+1} = (p+qy_n)/(1+y_n+ry_{n-k})\), \(n=0,1,\dots\), where \(p,q,r\) are positive numbers. They show that the unique positive equilibrium globally attracts all positive values of the parameters. The obtained results improve previous ones in this direction.


39A11 Stability of difference equations (MSC2000)
39A20 Multiplicative and other generalized difference equations
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