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Nonautonomous Dynamical Systems

formerly Nonautonomous and Stochastic Dynamical Systems

Editor-in-Chief: Diagana, Toka

Managing Editor: Cánovas, Jose


Mathematical Citation Quotient (MCQ) 2017: 0.71

Open Access
Online
ISSN
2353-0626
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Estimates for Solutions of Differential Equations in a Banach Space via Commutators

Michael Gil’
Published Online: 2018-02-28 | DOI: https://doi.org/10.1515/msds-2018-0001

Abstract

In a Banach space we consider the equation dx(t)/dt = (A + B(t))×(t) (t ≥ 0), where A is a constant bounded operator, and B(t) is a bounded variable operator.Norm estimates for the solutions of the considered equation are derived in terms of the commutator AB(t) − B(t)A. These estimates give us sharp stability conditions. Our results are new even in the finite dimensional case.We also discuss applications of the obtained results to a class of integro-differential equations.

Keywords: Banach space; differential equation; solution estimates; stability; integro-differential equation

MSC 2010: 34G10; 34D05; 34D20

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About the article

Received: 2017-05-24

Accepted: 2018-01-26

Published Online: 2018-02-28


Citation Information: Nonautonomous Dynamical Systems, Volume 5, Issue 1, Pages 1–7, ISSN (Online) 2353-0626, DOI: https://doi.org/10.1515/msds-2018-0001.

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© 2018. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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