Boundary Value Problems for Delay Differential Systems

Advances in Difference Equations

A. Boichuk³  M. Rikov⁴  J. Diblk⁵  D. Khusainov⁶ 

[1] Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering, Brno University of Technology, Brno, Czech Republic;Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno, Czech Republic;Department of Mathematics, Faculty of Science, University of ŽInstitute of Mathematics, National Academy of Sciences of Ukraine, Kyiv, Ukraine;ilina, Žilina, Slovakia

关键词: Parametric Family;    Homogeneous Problem;    Dimensional Matrix;    Dimensional Family;    Cauchy Matrix;   

DOI  :  10.1155/2010/593834

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

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) not coinciding with the number of unknowns of a differential system with a single delay. As an example of application of the results derived, the problem of bifurcation of solutions of boundary-value problems for systems of ordinary differential equations with a small parameter and with a finite number of measurable delays of argument is considered.

【 授权许可】

CC BY