Geodesic
Stability of solutions to differential equations with several variable delays.~II
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 3-15.

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 addmissible values of delays. We investigate domains in the parameter space, whose points correspond to families of equations that possess certain properties, which are uniform and exponential stabilities of solutions, and the property of the fundamental solution of an equation to have fixed sign. Necessary and sufficient conditions for a family of equations to have these properties are obtained in the explicit form.
Keywords: functional differential equation, varying delay, several delays, fixed sign, stability, fundamental solution. 
@article{IVM_2013_7_a0,
     author = {V. V. Malygina and K. M. Chudinov},
     title = {Stability of solutions to differential equations with several variable {delays.~II}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--15},
     publisher = {mathdoc},
     number = {7},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2013_7_a0/}
}
TY  - JOUR
AU  - V. V. Malygina
AU  - K. M. Chudinov
TI  - Stability of solutions to differential equations with several variable delays.~II
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2013
SP  - 3
EP  - 15
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2013_7_a0/
LA  - ru
ID  - IVM_2013_7_a0
ER  - 
%0 Journal Article
%A V. V. Malygina
%A K. M. Chudinov
%T Stability of solutions to differential equations with several variable delays.~II
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2013
%P 3-15
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2013_7_a0/
%G ru
%F IVM_2013_7_a0
V. V. Malygina; K. M. Chudinov. Stability of solutions to differential equations with several variable delays.~II. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2013), pp. 3-15. http://geodesic.mathdoc.fr/item/IVM_2013_7_a0/

[1] Malygina V. V., Chudinov K. M., “Ustoichivost reshenii differentsialnykh uravnenii s neskolkimi peremennymi zapazdyvaniyami. I”, Izv. vuzov. Matem., 2013, no. 6, 25–36

[2] Maksimov V. P., Rakhmatullina L. F., “O predstavlenii resheniya lineinogo funktsionalno-differentsialnogo uravneniya”, Differents. uravneniya, 9:6 (1973), 1026–1036 | MR | Zbl

[3] Azbelev N. V., Simonov P. M., “Ustoichivost uravnenii s zapazdyvayuschim argumentom”, Izv. vuzov. Matem., 1997, no. 6, 3–16 | MR | Zbl

[4] Azbelev N. V., Simonov P. M., Ustoichivost uravnenii s obyknovennymi proizvodnymi, Izd-vo Permsk. un-ta, Perm, 2001

[5] Berezansky L., Braverman E., “On oscillation of equations with distributed delay”, Z. Anal. Anwend., 20:2 (2001), 489–504 | MR | Zbl

[6] Tramov M. I., “Usloviya koleblemosti reshenii differentsialnykh uravnenii pervogo poryadka s zapazdyvayuschim argumentom”, Izv. vuzov. Matem., 1975, no. 5, 92–96 | MR | Zbl

[7] Györi I., Ladas G., Oscillation theory of delay differential equations, Clarendon Press, Oxford, 1991 | MR

[8] Gopalsamy K., Stability and oscillation in delay differential equations of population dynamics, Kluwer Academic Publishers, Dordrecht–Boston–London, 1992 | MR | Zbl

[9] Erbe L. N., Kong Q., Zhang B. G., Oscillation theory for functional-differential equations, Marcel Dekker, New York–Basel, 1995 | MR