Electronic Journal of Differential Equations,
Conference 06 (2001), pp. 225--241.

Title: Exponential dichotomies for  linear systems with impulsive effects.

Authors: Raul Naulin (Univ. de Oriente, Cumana, Venezuela)
 
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.