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arXiv · 1707.08909

Global Lipschitz Invariant Center Manifolds for ODEs with Generalized Trichotomies

António J. G. Bento·Cristina Tomás da Costa
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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.

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António J. G. Bento, Cristina Tomás da Costa. 2017-07-27. Global Lipschitz Invariant Center Manifolds for ODEs with Generalized Trichotomies. https://arxiv.org/abs/1707.08909

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