Geodesic
Exponent estimation for stable solutions of a certain class of differential-difference equations
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 67-79.

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

For differential-difference equations with a positive fundamental solution we obtain exponential stability conditions with exact estimates of the exponent and coefficient of decay. The estimates are determined through the largest of two possible real roots of the characteristic function. We show that it is possible to obtain exact estimates for any solution, based on an estimate of the fundamental solution, and taking into account the norm of an initial function. We find two-sided estimates of the fundamental solution in the case when the parameters of an equation are given at intervals.
Keywords: functional differential equation, fundamental solution, exponential stability, exponent estimate. 
@article{IVM_2021_12_a5,
     author = {V. V. Malygina},
     title = {Exponent estimation for stable solutions of a certain class of differential-difference equations},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {67--79},
     publisher = {mathdoc},
     number = {12},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_12_a5/}
}
TY  - JOUR
AU  - V. V. Malygina
TI  - Exponent estimation for stable solutions of a certain class of differential-difference equations
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2021
SP  - 67
EP  - 79
IS  - 12
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2021_12_a5/
LA  - ru
ID  - IVM_2021_12_a5
ER  - 
%0 Journal Article
%A V. V. Malygina
%T Exponent estimation for stable solutions of a certain class of differential-difference equations
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2021
%P 67-79
%N 12
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2021_12_a5/
%G ru
%F IVM_2021_12_a5
V. V. Malygina. Exponent estimation for stable solutions of a certain class of differential-difference equations. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 12 (2021), pp. 67-79. http://geodesic.mathdoc.fr/item/IVM_2021_12_a5/

[1] Pertsev N. V., “Primenenie M-matrits dlya postroeniya eksponentsialnykh otsenok reshenii zadachi Koshi dlya nekotorykh sistem lineinykh raznostnykh i differentsialnykh uravnenii”, Matem. tr., 16:2 (2013), 111–141 | Zbl

[2] Demidenko G. V., Matveeva I. I., “Asimptoticheskie svoistva reshenii differentsialnykh uravnenii s zapazdyvayuschim argumentom”, Vestn. NGU. Ser. Matem., mekhan., informatika, 5:3 (2005), 20–28 | Zbl

[3] Liz E., Pituk M., “Exponential stability in a scalar functional-differential equation”, J. Inequal. Appl., 2006, 37195 | Zbl

[4] Azbelev N. V., Maksimov V. P., Rakhmatullina L. F., Vvedenie v teoriyu funktsionalno-differentsialnykh uravnenii, Nauka, M., 1991

[5] Myshkis A. D., Lineinye differentsialnye uravneniya s zapazdyvayuschim argumentom, Nauka, M., 1972

[6] Ryabov Yu. A., “Nekotorye asimptoticheskie svoistva lineinykh sistem s malym zapazdyvaniem po vremeni”, DAN SSSR, 151:1 (1963), 52–54 | Zbl

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

[8] Agarwal R. P., Berezansky L., Braverman E., Domoshnitsky A., Nonoscillation theory of functional differential equations with applications, Springer, New York, 2012 | Zbl

[9] Chudinov K. M., “Asimptotika polozhitelnykh reshenii avtonomnogo diffrentsialnogo uravneniya s posledeistviem”, Sovremennye metody prikl. matem., teorii upravleniya i kompyuternykh tekhn., PMTUKT-2015, sb. tr. konf. (Voronezh, 21–26 sent. 2015 g.), Nauchn. kniga, Voronezh, 2015, 386–388

[10] Sabatulina T., Malygina V., “On positiveness of the fundamental solution for a linear autonomous differential equation with distributed delay”, Electron. J. Qual. Theory Differ. Equat., 2014, 61 | Zbl

[11] Lavrentev M. A., Shabat B. V., Metody teorii funktsii kompleksnogo peremennogo, Nauka, M., 1987

[12] Elsgolts L. E., Norkin S. B., Vvedenie v teoriyu differentsialnykh uravnenii s otklonyayuschimsya argumentom, Nauka, M., 1971

[13] Kheil Dzh., Teoriya funktsionalno-differentsialnykh uravnenii, Mir, M., 1984

[14] Malygina V. V., Chudinov K. M., “Ustoichivost reshenii differentsialnykh uravnenii s neskolkimi peremennymi zapazdyvaniyami. II”, Izv. vuzov. Matem., 2013, no. 7, 3–15 | Zbl

[15] Sabatulina T. L., “Oscillating and sign-definite solutions to autonomous functional-differential equations”, J. Math. Sci., 230:5 (2018), 766–769 | DOI | Zbl

[16] Györi I., Ladas G., Oscillation theory of delay differential equations: with applications, Clarendon Press, Oxford, 1991 | Zbl