Geodesic
Stability of solutions to differential equations with several variable delays.~I
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 25-36

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider a class of scalar linear differential equations with several variable delays and constant coefficients. A family of equations of the class is defined by coefficients and maximum admissible values of delays. We obtain conditions that are necessary and sufficient for the stability of solutions to all equations of the family. It is ascertained that the conditions are determined entirely by properties of the solution to the initial problem for an autonomous equation that belongs to the family. Some alternatives of required conditions are obtained in the form of estimates for solutions to autonomous equations in a finite interval.
Keywords: functional differential equation, varying delay, several delays, stability, the Cauchy function. 
@article{IVM_2013_6_a2,
     author = {V. V. Malygina and K. M. Chudinov},
     title = {Stability of solutions to differential equations with several variable {delays.~I}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {25--36},
     publisher = {mathdoc},
     number = {6},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_6_a2/}
}
TY  - JOUR
AU  - V. V. Malygina
AU  - K. M. Chudinov
TI  - Stability of solutions to differential equations with several variable delays.~I
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 25
EP  - 36
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_6_a2/
LA  - ru
ID  - IVM_2013_6_a2
ER  - 
%0 Journal Article
%A V. V. Malygina
%A K. M. Chudinov
%T Stability of solutions to differential equations with several variable delays.~I
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 25-36
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_6_a2/
%G ru
%F IVM_2013_6_a2
V. V. Malygina; K. M. Chudinov. Stability of solutions to differential equations with several variable delays.~I. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2013), pp. 25-36. http://geodesic.mathdoc.fr/item/IVM_2013_6_a2/