This corresponds to the existence of a "generalized" exponential dichotomy, which is known to be robust.
Complete characterizations for the exponential dichotomy of cocycles are also obtained.
We also show that the constants determining the nonuniform exponential contraction or nonuniform exponential dichotomy vary continuously with the perturbation.
In this way, the only unknowns of the solving system, characterized by an exponential dichotomy, are represented by shear forces transmitted along joints.
We prove a result ensuring the existence of an almost automorphic solution for both equations, assuming that the associated homogeneous equation of this system admits an exponential dichotomy.
Moreover, we involve a concept of a "no past" exponential dichotomy for cocycles weaker than the classical concept defined by Sacker and Sell (1994) in [23].
A "discrete" technique for investigating the evolutionary semigroup is developed and applied in describing the hyperbolicity (exponential dichotomy) of the nonautonomous equation.
We then apply our results to study the robustness of the exponential dichotomy of evolution families on a half-line under small perturbations.
We construct topological conjugacies between linear and nonlinear evolution operators that admit either a nonuniform exponential contraction or a nonuniform exponential dichotomy.
admits an exponential dichotomy on.
admits an exponential dichotomy on Z.
