Asymptotic representation of solutions of system of linear differential equations with slowly varying coefficients

1974 ◽  
Vol 25 (4) ◽  
pp. 414-423
Author(s):  
N. I. Shkil ◽  
V. K. Grigorenko
Keyword(s):  
Differential Equations ◽  
Asymptotic Representation ◽  
Linear Differential Equations ◽  
Varying Coefficients ◽  
Asymptotic Representation Of Solutions ◽  
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.

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