USA-Chile Workshop on Nonlinear Analysis,
Electron. J. Diff. Eqns., Conf. 06, 2001, pp. 225-241.

Exponential dichotomies for linear systems with impulsive effects

Raul Naulin

Abstract:
In this paper we give conditions for the existence of a dichotomy for the impulsive equation
$$\displaylines{ \mu(t,\varepsilon) x'= A(t)x, \; t \neq t_k,\cr x(t_k^+ )= C_k x(t_k^-)\,, }$$
where $\mu(t,\varepsilon)$ is a positive function such that $\lim\mu(t,\varepsilon)=0$ in some sense. The results are expressed in terms of the properties of the eigenvalues of matrices $A(t)$, the properties of the eigenvalues of matrices $\{C_k\}$ and the location of the impulsive times $\{t_k\}$ in $[0, \infty)$.

Published January 8, 2001.
Math Subject Classifications: 34A05, 34E05.
Key Words: Impulsive linear systems, singularly perturbed impulsive systems, dichotomies, splitting of impulsive systems.

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Raul Naulin
Departamento de Matematicas, Universidad de Oriente
Apartado 245, Cumana 6101-A, Venezuela
e-mail: rnaulin@cumana.sucre.udo.edu.ve
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