scholarly journals Optimal conditions for unique solvability of the Cauchy problem for first order linear functional differential equations

2002 ◽  
Vol 52 (3) ◽  
pp. 513-530 ◽  
Author(s):  
E. Bravyi ◽  
R. Hakl ◽  
A. Lomtatidze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Unique Solvability ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Optimal Conditions ◽  
Order Linear ◽  
First Order ◽  
The Cauchy Problem ◽  
Functional Differential

scholarly journals On linear singular functional-differential equations in one functional space

2004 ◽  
Vol 2004 (7) ◽  
pp. 567-575 ◽  
Author(s):  
Andrei Shindiapin
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Functional Space ◽  
Integrable Functions ◽  
The Cauchy Problem ◽  
Functional Differential ◽  
Space Of Integrable Functions ◽  
Special Space

We use a special space of integrable functions for studying the Cauchy problem for linear functional-differential equations with nonintegrable singularities. We use the ideas developed by Azbelev and his students (1995). We show that by choosing the functionψgenerating the space, one can guarantee resolubility and certain behavior of the solution near the point of singularity.

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