Differential and Integral Equations

On exponential stability of functional differential equations with variable impulse perturbations

S.M. Afonso, E.M. Bonotto, and M. Federson

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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.

Article information

Source
Differential Integral Equations, Volume 27, Number 7/8 (2014), 721-742.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1399395750

Mathematical Reviews number (MathSciNet)
MR3200761

Zentralblatt MATH identifier
1340.34303

Subjects
Primary: 34K20: Stability theory 34K45: Equations with impulses 26A39: Denjoy and Perron integrals, other special integrals

Citation

Afonso, S.M.; Bonotto, E.M.; Federson, M. On exponential stability of functional differential equations with variable impulse perturbations. Differential Integral Equations 27 (2014), no. 7/8, 721--742. https://projecteuclid.org/euclid.die/1399395750


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