  We study some classes of semi-linear differential equations including both
well-posed and ill-posed cases that can generate cocycles (or cocycle
correspondences with generating cocycles). Under exponential dichotomy
condition with other mild assumptions, we investigate the existence,
persistence and regularity of different types of invariant manifolds for these
differential equations based on our previous works about invariant manifold
theory for abstract `generalized dynamical systems': invariant graphs (global
version) and normally hyperbolic invariant manifolds (local version); brief
summaries of those works are also given.
