Differential and Integral Equations
- Differential Integral Equations
- Volume 27, Number 7/8 (2014), 721-742.
On exponential stability of functional differential equations with variable impulse perturbations
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.
Differential Integral Equations, Volume 27, Number 7/8 (2014), 721-742.
First available in Project Euclid: 6 May 2014
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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