Uniform Asymptotic Stability of Evolutionary Processes in a Banach Space

Datko-Pazy conditions for nonuniform exponential stability

“…In particular, Pazy [19] proved that the conclusion of Datko's theorem is valid even if we replace L 2 (R + , X) with any L p (R + , X), p ∈ [1, ∞). Furthermore, Datko [9] obtained related results which deal with the exponential stability of continuous-time evolution families (see [34] for related results in the case of discrete time). The far-reaching generalization of Datko's theorem for evolution families was obtained by Rolewicz [27] (see also [6,31]).…”

Functionals on function and sequence spaces connected with the exponential stability of evolutionary processes

“…Also using a discrete time argument, an extension of the well-known Datko's result [3] was obtained in [13].…”

Polynomial stability of evolution operators in Banach spaces

“…Characterizations for exponential stability properties of strongly measurable evolution operator with uniform growth are given in [1,6,7] for u.e.s, respectively in [4,8] and [10] for e.s, respectively in [2,3,8] and [9] for B.V.e.s.…”