Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article Boundary Value Problems for Delay Differential Systems | Hindawi Publishing Corporation Advances in Difference Equations Volume 2010 Article ID 593834 20 pages doi 2010 593834 Research Article Boundary Value Problems for Delay Differential Systems A. Boichuk 1 2 J. Diblik 3 4 D. Khusainov 5 and M. RuziCkova1 1 Department of Mathematics Faculty of Science University ofZilina Univerzitnd 8215 1 01026 Zilina Slovakia 2 Institute of Mathematics National Academy of Sciences of Ukraine Tereshchenkovskaya Str. 3 01601 Kyiv Ukraine 3 Department of Mathematics and Descriptive Geometry Faculty of Civil Engineering Brno University of Technology Veveri 331 95 60200 Brno Czech Republic 4 Department of Mathematics Faculty of Electrical Engineering and Communication Brno University of Technology Technicka 8 61600 Brno Czech Republic 5 Department of Complex System Modeling Faculty of Cybernetics Taras Shevchenko National University of Kyiv Vladimirskaya Str. 64 01033 Kyiv Ukraine Correspondence should be addressed to A. Boichuk boichuk@ Received 16 January 2010 Revised 27 April 2010 Accepted 12 May 2010 Academic Editor Agacik Zafer Copyright 2010 A. 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. Conditions are derived of the existence of solutions of linear Fredholm s boundary-value problems for systems of ordinary differential equations with constant coefficients and a single delay assuming that these solutions satisfy the initial and boundary conditions. Utilizing a delayed matrix exponential and a method of pseudoinverse by Moore-Penrose matrices led to an explicit and analytical form of a criterion for the existence of solutions in a relevant space and moreover to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions defined by a linear vector functional
