Asymptotic behavior of solutions of Volterra difference equations with finite linear part
For the solutions of the nonlinear Volterra difference equation NEWLINE\[NEWLINE\Delta x_n+ \sum^N_{m=0} a_{nm}x_{n-m} +f(n,x_{n_0}, \dots,x_n),\;n\geq n_0,NEWLINE\]NEWLINE 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.
scientific article; zbMATH DE number 1693369