On the exact boundaries of the stability domain of linear differential equations with distributed delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 19-28.

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

For a differential equation with a distributed varying delay, sufficient criterions of asymptotic and uniform stability of solutions are obtained. The constructed examples demonstrate exactness of the boundary of the obtained stability domain.
Keywords: functional differential equations, distributed delay, stability.
@article{IVM_2008_7_a2,
     author = {V. V. Malygina},
     title = {On the exact boundaries of the stability domain of linear differential equations with distributed delay},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {19--28},
     publisher = {mathdoc},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2008_7_a2/}
}
TY  - JOUR
AU  - V. V. Malygina
TI  - On the exact boundaries of the stability domain of linear differential equations with distributed delay
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2008
SP  - 19
EP  - 28
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2008_7_a2/
LA  - ru
ID  - IVM_2008_7_a2
ER  - 
%0 Journal Article
%A V. V. Malygina
%T On the exact boundaries of the stability domain of linear differential equations with distributed delay
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2008
%P 19-28
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2008_7_a2/
%G ru
%F IVM_2008_7_a2
V. V. Malygina. On the exact boundaries of the stability domain of linear differential equations with distributed delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2008), pp. 19-28. http://geodesic.mathdoc.fr/item/IVM_2008_7_a2/

[1] Myshkis A. D., “O resheniyakh lineinykh odnorodnykh differentsialnykh uravnenii pervogo poryadka ustoichivogo tipa s zapazdyvayuschim argumentom”, Matem. sb., 28:3 (1951), 641–658 | MR | Zbl

[2] Yorke J. A., “Asymptotic stability for one dimensional differential-delay equations”, J. Different. Equat., 7:1 (1970), 189–202 | DOI | MR | Zbl

[3] Yoneyama T., “On the $3/2$ stability theorem for one dimensional delay-differential equations”, J. Math. Anal. Appl., 125:1 (1987), 161–173 | DOI | MR | Zbl

[4] Malygina V. V., “Nekotorye priznaki ustoichivosti funktsionalno-differentsialnykh uravnenii, razreshennykh otnositelno proizvodnoi”, Izv. vuzov. Matematika, 1992, no. 7, 46–53 | MR | Zbl

[5] Malygina V. V., “Nekotorye priznaki ustoichivosti uravnenii s zapazdyvayuschim argumentom”, Differents. uravneniya, 28:10 (1992), 1716–1723 | MR | Zbl

[6] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991, 277 pp. | MR | Zbl

[7] Azbelev N. V., Simonov P. M., Ustoichivost uravnenii s obyknovennymi proizvodnymi, Izd-vo Permsk. un-ta, Perm, 2001, 229 pp. | MR

[8] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Per. s angl., Mir, M., 1984, 424 pp. | MR

[9] Vagina M. Yu., “Logisticheskaya model s zapazdyvayuschim usredneniem”, Avtomatika i telemekhanika, 2003, no. 4, 167–173 | MR | Zbl

[10] Sabatulina T. L., Malygina V. V., “Ob asimptoticheskoi ustoichivosti odnogo klassa sistem differentsialnykh uravnenii s raspredelennym zapazdyvaniem”, Vestn. Permsk. gos. tekhn. un-ta. Prikladnaya matem. i mekh., no. 1, Perm, 2004, 114–120 | MR

[11] Malygina V. V., “O polozhitelnosti funktsii Koshi lineinogo uravneniya s raspredelennym zapazdyvaniem”, Vestn. Permsk. gos. tekhn. un-ta, no. 1, Perm, 2006, 80–83

[12] Gusarenko S. A., “Priznaki razreshimosti zadach o nakoplenii vozmuschenii dlya funktsionalno-differentsialnykh uravnenii”, Funktsionalno-differents. uravneniya, Mezhvuz. sb. nauchn. tr., Perm, 1987, 30–40 | MR | Zbl

[13] Amemiya T., “On the delay-independent stability of a delayed differential equations of $1$st order”, J. Math. Anal. Appl., 142:1 (1989), 13–25 | DOI | MR | Zbl

[14] Ladas G., Sficas Y. G., Stavroulakis I. P., “Asymptotic behaviour of solutions of retarded differential equations”, Proc. Amer. Math. Soc., 88:2 (1983), 247–253 | DOI | MR | Zbl