Almost periodic solutions of delay difference systems (Q1855805)

Consider the system of delay difference equations \[ x(n+ 1)= f(n, x(n)),\qquad n\in\mathbb{Z}, \] where \(f(n,\varphi)\) is almost periodic in \(n\) uniformly for \(\|\varphi\|\leq B\). Under some assumptions, to complicate to be presented here, the authors show that if the system is stable with respect to so-called disturbance on \(f\), then the solution to the system is almost periodic, resp. asymptotically almost periodic etc. The existence and uniqueness of such solutions is proved using some properties of Lyapunov functionals.