A general version of the retract method for discrete equations (Q884901)

The topological method of \textit{T. Wazewski} [Ann. Soc. Polon. Math. 20, 279--313 (1948; Zbl 0032.35001)] on asymptotic behavior of solutions is extended to difference equations of the form \[ u_{k+1}=F_k(u_k) \] The idea is to obtain the existence of a solution entirely lying in some open set given a priori. This is proved by the retract method through finding the adequate initial conditions. Two examples in the linear ``time varying'' class are given.