## Asymptotic behavior of a nonlinear difference equation.(English)Zbl 1049.39012

The author investigates the asymptotic behavior of solutions of scalar difference equations of the form $$x_{n+1} = f(x_n,\dots, x_{n-k})$$ where $$f$$ satisfies some estimates at infinity. The obtained results extend several well known ones.

### MSC:

 39A11 Stability of difference equations (MSC2000)

### Keywords:

asymptotic behavior; difference equations