Open Access
January, 2015 Robustness of noninvertible dichotomies
J. Math. Soc. Japan 67(1): 293-317 (January, 2015). DOI: 10.2969/jmsj/06710293


We establish the robustness of exponential dichotomies for evolution families of linear operators in a Banach space, in the sense that the existence of an exponential dichotomy persists under sufficiently small linear perturbations. We note that the evolution families may come from nonautonomous differential equations involving unbounded operators. We also consider the general case of a noninvertible dynamics, thus including several classes of functional equations and partial differential equations. Moreover, we consider the general cases of nonuniform exponential dichotomies and of dichotomies that may exhibit stable and unstable behaviors with respect to arbitrary asymptotic rates $e^{c\rho(t)}$ for some function $\rho(t)$.


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Luis BARREIRA. Claudia VALLS. "Robustness of noninvertible dichotomies." J. Math. Soc. Japan 67 (1) 293 - 317, January, 2015.


Published: January, 2015
First available in Project Euclid: 22 January 2015

zbMATH: 1347.34090
MathSciNet: MR3304023
Digital Object Identifier: 10.2969/jmsj/06710293

Primary: 34D99 , 37C75

Keywords: exponential dichotomies , robustness

Rights: Copyright © 2015 Mathematical Society of Japan

Vol.67 • No. 1 • January, 2015
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