Global Lipschitz Invariant Center Manifolds for ODEs with Generalized Trichotomies

António J. G. Bento; Cristina Tomás da Costa

paper

Global Lipschitz Invariant Center Manifolds for ODEs with Generalized Trichotomies

arXiv:1707.08909

Abstract

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