Global Lipschitz Invariant Center Manifolds for ODEs with Generalized\n Trichotomies

2017/07/27 by António J. G. Bento, Bento, António J. G., Cristina Tomás da Costa +1
Mathematics · #Differential Equations and Numerical Methods #Nonlinear Differential Equations Analysis #Advanced Differential Equations and Dynamical Systems

paper · pdf · doi:10.48550/arxiv.1707.08909

Abstract

In a Banach space, assuming that a linear nonautonomous differential equation\nv'=A(t)v admits a very general type of trichotomy, we establish conditions\nfor the existence of global Lipschitz invariant center manifold of the\nperturbed equation v'=A(t)v+f(t,v). Our results not only improve results\nalready existing in the literature, as well include new cases.\n

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