Barbashin-type conditions for exponential stability of linear cocycles

Integral Characterizations for Uniform Stability with Growth Rates in Banach Spaces

“…We remark that the sets of growth rates considered in this paper are different from those studied in [19]. Moreover, the results obtained for the exponential and polynomial cases are also distinct from those presented in the papers [6][7][8][9][10][11][12][13][14][15].…”

“…Barbashin [1] and R. Datko [4]. After the seminal research of Barbashin and Datko, there has been a large number of papers devoted to this subject [5][6][7][8][9][10][11][12]. Generalizations of Barbashin and Datko's results for the case of the polynomial behaviors are given in [13][14][15][16].…”

Some Datko and Barbashin type characterizations for the uniform \(h\)-instability of evolution families

“…After the path-breaking research of Barbashin and Datko, through the usage of Datko-Pazy theorem, admissibility, Banach function spaces, Lyapunov functions, discrete-time methods and other ways, there has been numerous extensions and generalizations devoted to this area (see [2,6,9,12,13,14,15,16,17,18,22,23,24,27,30,31] and the references therein). For instance, in [12] Dragičević obtained some continuous and discrete versions of Datko type theorem for the concept of the exponential stability in average.…”