## Asymptotic behavior of solutions of Volterra difference equations with finite linear part.(English)Zbl 0994.39006

For the solutions of the nonlinear Volterra difference equation $\Delta x_n+ \sum^N_{m=0} a_{nm}x_{n-m} +f(n,x_{n_0}, \dots,x_n),\;n\geq n_0,$ with prescribed initial values $$x_{n_0-N}, \dots,x_{n_0}$$ and $$f(n,0, \dots,0)=0$$ boundedness and stability properties as well as asymptotic formulas are established.

### MSC:

 39A11 Stability of difference equations (MSC2000)