Boundedness and stability of solutions to difference equations (Q1602779)

The authors obtain some stability and boundedness results for difference equations of order \(k\) in the form \(y_{n+1}=f(n,y_n)\), where \(f:\mathbb{Z}^+\times \mathbb{R}^k\to \mathbb{R}^k\), assuming that either \(f\) or the function \(\varphi\) that defines the solution operator (\(y_n=\varphi(n,y_0), n\geq 1\)) satisfies a Lipschitz (or local Lipschitz) condition with respect to the second variable.