Admissibility on the half line for evolution families

作者：Barreira Luis^*; Dragicevic Davor; Valls Claudia

来源：Journal d Analyse Mathematique, 2017, 132(1): 157-176.

DOI：10.1007/s11854-017-0017-4

For an arbitrary evolution family, we consider the notion of an exponential dichotomy with respect to a family of norms and characterize it completely in terms of the admissibility of bounded solutions, that is, the existence of a unique bounded solution for each bounded perturbation. In particular, by considering a family of Lyapunov norms, we recover the notion of a nonuniform exponential dichotomy. As a nontrivial application of the characterization, we establish the robustness of the notion of an exponential dichotomy with respect to a family of norms under sufficiently small Lipschitz and C (1) parameterized perturbations. Moreover, we establish the optimal regularity of the dependence on the parameter of the projections onto the stable spaces of the perturbation.

• 出版日期2017-6