Discrete asymptotic behaviors for skew-evolution semiflows on Banach spaces

The paper emphasizes asymptotic behaviors, as stability and instability for skew-evolution semiflows, defined by means of evolution semiflows and evolution cocycles and which can be considered generalizations for evolution operators and skew-product semiflows. The unified treatment for the characterization of the studied properties in the nonuniform case is given in discrete time. The results, which are characterizations of Datko, Barbashin and Rolewicz type for stability and instability and were presented in [8] and [9], can be considered generalizations of those obtained for evolution operators and skew-product semiflows in Banach spaces, in continuous and discret time in [5] and [6]. Characterizations for the nonuniform stability for evolution processes were given in [1] and for difference equations in [2], as well as in [4] for evolution families. For evolution operators, characterizations for the nonuniform instability were obtained in [3] and [7].