scholarly journals A Note on Generalized Solution of a Cauchy Problem Given by a Nonhomogeneous Linear Differential System

2020 ◽  
Vol 17 (2) ◽  
pp. 24-30
Author(s):  
Marcel Bogdan

AbstractGeneralized solution of a Cauchy problem given by a nonhomogeneous linear differential system is recovered to this approach. It considers the case of the free term having at most countable number of discontinuity points. The method, called successive approach, uses the solution on the previous interval (except the first one) for the condition on the given interval. The sequence of commands for a computer algebra system to this method is given.

1996 ◽  
Vol 3 (5) ◽  
pp. 475-485
Author(s):  
I. Kiguradze

Abstract The conditions ensuring the correctness of the Cauchy problem on the nonnegative half-axis R + are found, where P : R + → R n×n and q : R + → Rn are locally summable matrix and vector functions, respectively, t 0 ∈ R + and c 0 ∈ Rn .


Author(s):  
P. Ch. Tsamatos

AbstractThis paper is concerned with the neutral type differential system with derivating arguments. By decomposing the space of initial functions into classes, it is derived that, for each class, the space of corresponding solutions is of finite dimension. The case of common fixed points of the arguments is also studied.


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