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July/August 2014 On exponential stability of functional differential equations with variable impulse perturbations
S.M. Afonso, E.M. Bonotto, M. Federson
Differential Integral Equations 27(7/8): 721-742 (July/August 2014).

Abstract

We consider a class of functional differential equations subject to perturbations, which vary in time, and we study the exponential stability of solutions of these equations using the theory of generalized ordinary differential equations and Lyapunov functionals. We introduce the concept of variational exponential stability for generalized ordinary differential equations and we develop the theory in this direction by establishing conditions for the trivial solutions of generalized ordinary differential equations to be exponentially stable. Then, we apply the results to get corresponding ones for impulsive functional differential equations. We also present an example of a delay differential equation with Perron integrable right-hand side where we apply our result.

Citation

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S.M. Afonso. E.M. Bonotto. M. Federson. "On exponential stability of functional differential equations with variable impulse perturbations." Differential Integral Equations 27 (7/8) 721 - 742, July/August 2014.

Information

Published: July/August 2014
First available in Project Euclid: 6 May 2014

zbMATH: 1340.34303
MathSciNet: MR3200761

Subjects:
Primary: 26A39, 34K20, 34K45

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 7/8 • July/August 2014
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