scholarly journals Representation of Solutions of Systems of Linear Differential Equations with Multiple Delays and Linear Parts Given by Nonpermutable Matrices

2017 ◽  
Vol 228 (3) ◽  
pp. 276-289 ◽  
Author(s):  
M. Medved’ ◽  
M. Pospíšil
Keyword(s):  
Differential Equations ◽  
Linear Differential Equations ◽  
Multiple Delays ◽  
Representation Of Solutions ◽  
Linear Differential

scholarly journals REPRESENTATION OF SOLUTIONS OF SYSTEMS OF LINEAR DIFFERENTIAL EQUATIONS WITH MULTIPLE DELAYS AND NONPERMUTABLE VARIABLE COEFFICIENTS

2020 ◽  
Vol 25 (2) ◽  
pp. 303-322
Author(s):  
Michal Pospíšil
Keyword(s):  
Differential Equations ◽  
Variable Coefficients ◽  
Linear Differential Equations ◽  
Multiple Delays ◽  
Matrix Coefficients ◽  
Representation Of Solutions ◽  
The Matrix ◽  
Constant Coefficients ◽  
Linear Differential ◽  
Delay Differential

Solutions of nonhomogeneous systems of linear differential equations with multiple constant delays are explicitly stated without a commutativity assumption on the matrix coefficients. In comparison to recent results, the new formulas are not inductively built, but depend on a sum of noncommutative products in the case of constant coefficients, or on a sum of iterated integrals in the case of time-dependent coefficients. This approach shall be more suitable for applications.Representation of a solution of a Cauchy problem for a system of higher order delay differential equations is also given.

scholarly journals Representation of a Solution of the Cauchy Problem for an Oscillating System with Multiple Delays and Pairwise Permutable Matrices

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Josef Diblík ◽  
Michal Fečkan ◽  
Michal Pospíšil
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Initial Value Problem ◽  
Linear Differential Equations ◽  
Multiple Delays ◽  
Initial Value ◽  
Matrix Polynomials ◽  
The Cauchy Problem ◽  
Nonhomogeneous System ◽  
Linear Differential

Nonhomogeneous system of linear differential equations of second order with multiple different delays and pairwise permutable matrices defining the linear parts is considered. Solution of corresponding initial value problem is represented using matrix polynomials.

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