Integral conditions for exponential dichotomy: A nonlinear approach

We give new necessary and sufficient integral conditions for the existence of exponential dichotomy of skew-product flows. Our methods are based on the structure of the associated stable subspace and unstable subspace. We propose a nonlinear approach, extending the study of exponential stability in terms of integral conditions to the case of uniform exponential dichotomy. We apply the main results to the study of uniform exponential dichotomy of non-autonomous systems.