Geodesic
Asymptotic integration of a system of differential equations with a large parameter in the critical case
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1043-1055 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

For a linear normal system of ordinary differential equations with rapidly oscillating coefficients in a critical case, the existence of a unique periodic solution is proved, its complete asymptotic expansion is constructed and justified, and Lyapunov stability and instability conditions are found. The asymptotic series constructed is shown to converge absolutely and uniformly to the solution. 
@article{ZVMMF_2011_51_6_a6,
     author = {Do Ngoc Thanh and V. B. Levenshtam},
     title = {Asymptotic integration of a~system of differential equations with a~large parameter in the critical case},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1043--1055},
     year = {2011},
     volume = {51},
     number = {6},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a6/}
}
TY  - JOUR
AU  - Do Ngoc Thanh
AU  - V. B. Levenshtam
TI  - Asymptotic integration of a system of differential equations with a large parameter in the critical case
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2011
SP  - 1043
EP  - 1055
VL  - 51
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a6/
LA  - ru
ID  - ZVMMF_2011_51_6_a6
ER  - 
%0 Journal Article
%A Do Ngoc Thanh
%A V. B. Levenshtam
%T Asymptotic integration of a system of differential equations with a large parameter in the critical case
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2011
%P 1043-1055
%V 51
%N 6
%U http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a6/
%G ru
%F ZVMMF_2011_51_6_a6
Do Ngoc Thanh; V. B. Levenshtam. Asymptotic integration of a system of differential equations with a large parameter in the critical case. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 51 (2011) no. 6, pp. 1043-1055. http://geodesic.mathdoc.fr/item/ZVMMF_2011_51_6_a6/

[1] Bogolyubov N. N., Mitropolskii Yu. A., Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974

[2] Vishik M. I., Lyusternik L. A., “Reshenie nekotorykh zadach o vozmuschenii v sluchae matrits i samosopryazhennykh i nesamosopryazhennykh differentsialnykh uravnenii”, Uspekhi matem. nauk, 15:3 (1960), 3–80 | MR | Zbl

[3] Levenshtam V. B., Differentsialnye uravneniya s bolshimi vysokochastotnymi slagaemymi, Izd-vo YuFU, Rostov-na-Donu, 2009

[4] Levenshtam V. B., “Asimptoticheskie razlozheniya periodicheskikh reshenii obyknovennykh differentsialnykh uravnenii s bolshimi vysokochastotnymi slagaemymi”, Differents. ur-niya, 41:1 (2008), 52–68 | MR

[5] Shtokolo I. Z., Lineinye differentsialnye uravneniya s peremennymi koeffitsientami, Izd-vo AN USSR, Kiev, 1960

[6] Vainberg M. M., Trenogin V. A., Teoriya vetvleniya reshenii nelineinykh uravnenii, Nauka, M., 1969

[7] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, Nauka, M., 1969

[8] Gantmakher F. R., Teoriya matrits, Nauka, M., 1988 | Zbl

[9] Krasnoselskii M. A., Operator sdviga po traektoriyam differentsialnykh uravnenii, Nauka, M., 1966