Global Lipschitz Invariant Center Manifolds for ODEs with Generalized Trichotomies

In a Banach space, assuming that a linear nonautonomous differential equation $v^{\mathrm{\prime }}=A(t)v$ admits a very general type of trichotomy, we establish conditions for the existence of global Lipschitz invariant center manifold of the perturbed equation $v^{\mathrm{\prime }}=A(t)v+f(t,v)$. Our results not only improve results already existing in the literature, as well include new cases.