Abstract
This article discusses difference dynamic systems (DDS). We want to get information about the existence and stability of solutions to difference dynamical systems. The effective method for such researching is the method of evaluating functions that depend on the known parameters included in the right side of the DDS. Moreover, it is possible to investigate DDS, in which the right-hand sides are not necessarily analytical. In this article, we explore a new analogue of Gronwall's result for DDS. In this paper, we investigate the problem of stability in the first approximation based on discrete inequalities.
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