Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Solutions of Linear Impulsive Differential Systems Bounded on the Entire Real Axis | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 494379 10 pages doi 2010 494379 Research Article Solutions of Linear Impulsive Differential Systems Bounded on the Entire Real Axis Alexandr Boichuk Martina Langerova and Jaroslava Skorikova Department of Mathematics Faculty of Science University ofZilina 010 26 Zilina Slovakia Correspondence should be addressed to Alexandr Boichuk boichuk@ 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. 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. The research in the theory of differential systems with impulsive action was originated by Myshkis and Samoilenko 1 Samoilenko and Perestyuk 2 Halanay and Wexler 3 and Schwabik et al. 4 . The ideas proposed in these works were developed and generalized in numerous other publications 5 . The aim of this contribution is using the theory of impulsive differential equations using the well-known results on the splitting index by Sacker 6 and by Palmer 7 on the Fredholm property of the problem of bounded solutions and using the theory of pseudoinverse matrices 5 8 to investigate in a relevant space the existence of solutions bounded on the entire real axis of linear differential systems with impulsive action. We consider the problem of existence and construction of solutions bounded on the entire real axis of linear .
