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

Medina, Rigoberto

Nonlinear Stud. 8, No. 1, 87-95 (2001).

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.

Reviewer: Lothar Berg (Rostock)

MSC:

39A11

Stability of difference equations (MSC2000)

Keywords:

asymptotic behaviour; bounded solution; nonlinear Volterra difference equation; stability; asymptotics