Journal of the Mathematical Society of Japan

Robustness of noninvertible dichotomies

Luis BARREIRA and Claudia VALLS

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Abstract

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 $\rho(t)$.

Article information

Source
J. Math. Soc. Japan, Volume 67, Number 1 (2015), 293-317.

Dates
First available in Project Euclid: 22 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.jmsj/1421936554

Digital Object Identifier
doi:10.2969/jmsj/06710293

Mathematical Reviews number (MathSciNet)
MR3304023

Zentralblatt MATH identifier
1347.34090

Subjects
Primary: 34D99: None of the above, but in this section 37C75: Stability theory

Keywords
exponential dichotomies robustness

Citation

BARREIRA, Luis; VALLS, Claudia. Robustness of noninvertible dichotomies. J. Math. Soc. Japan 67 (2015), no. 1, 293--317. doi:10.2969/jmsj/06710293. https://projecteuclid.org/euclid.jmsj/1421936554


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