Solvability of the Cauchy problem for higher-order linear functional differential equations

2012 ◽  
Vol 48 (4) ◽  
pp. 465-476 ◽  
Author(s):  
E. I. Bravyi
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Higher Order ◽  
Order Linear ◽  
The Cauchy Problem ◽  
Functional Differential

The weighted Cauchy problem for linear functional differential equations with strong singularities

2011 ◽  
Vol 18 (3) ◽  
pp. 577-586
Author(s):  
Zaza Sokhadze
Keyword(s):  
Cauchy Problem ◽  
Differential Equations ◽  
Linear Functional ◽  
Functional Differential Equations ◽  
Sufficient Conditions ◽  
Initial Point ◽  
Higher Order ◽  
Well Posedness ◽  
Deviating Arguments ◽  
Functional Differential

Abstract The sufficient conditions of well-posedness of the weighted Cauchy problem for higher order linear functional differential equations with deviating arguments, whose coefficients have nonintegrable singularities at the initial point, are found.

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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