Abstract
In this paper, by employing comparison technique and invariance properties of a positively limited set, we investigate the convergence of precompact orbits of a class of discrete-time semiflows. In particular, we consider the convergence of precompact orbits of discrete-time semiflows generated by some monotone mapping. We then apply these abstract results to a class of difference systems to obtain the large-time behavior of solutions. Our results improve and extend some existing ones.
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