On the asymptotic representation of solutions for systems of linear differential equations involving partial derivatives with retarded-time

1972 ◽  
Vol 23 (2) ◽  
pp. 151-161 ◽  
Author(s):  
S. F. Feshchenko ◽  
N. I. Shkil' ◽  
N. A. Sotnichenko
Keyword(s):  
Differential Equations ◽  
Asymptotic Representation ◽  
Linear Differential Equations ◽  
Retarded Time ◽  
Partial Derivatives ◽  
Asymptotic Representation Of Solutions ◽  
Representation Of Solutions ◽  
Linear Differential

Applications of a theorem by A. B. Shidlovski

1968 ◽  
Vol 305 (1481) ◽  
pp. 149-173 ◽  
Keyword(s):  
Differential Equations ◽  
Bessel Function ◽  
Linear Differential Equations ◽  
Euler’S Constant ◽  
Partial Derivatives ◽  
Arithmetic Properties ◽  
Linear Differential ◽  
Euler's Constant

Shidlovski’s deep theorem on Siegel E -functions satisfying systems of linear differential equations is applied in this paper to the study of the arithmetic properties of the partial derivatives C k (z) = 1/k!{∂/∂v} k J v (z)∣ v=0 ( k = 0,1,2,3) of the Bessel function J 0 (z) . As a by-product, expressions involving Euler’s constant γ and the constant ζ(3) are obtained for which the transcendency can be established.

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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