Advances in Difference Equations
Volume 2010 (2010), Article ID 494379, 10 pages
doi:10.1155/2010/494379
Research Article

Solutions of Linear Impulsive Differential Systems Bounded on the Entire Real Axis

Alexandr Boichuk, Martina Langerová, and Jaroslava Škoríková

Department of Mathematics, Faculty of Science, University of Žilina, 010 26 Žilina, Slovakia

Received 21 January 2010; Accepted 12 May 2010

Academic Editor: Leonid Berezansky

Copyright © 2010 Alexandr Boichuk et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the problem of existence and structure of solutions bounded on the entire real axis of nonhomogeneous linear impulsive differential systems. Under assumption that the corresponding homogeneous system is exponentially dichotomous on the semiaxes ℝ− and ℝ+ and by using the theory of pseudoinverse matrices, we establish necessary and sufficient conditions for the indicated problem.