Asymptotic analysis of certain systems of linear differential equations with a large parameter
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2144-2155 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Two classes of systems of linear ordinary differential equations containing high-frequency terms proportional to certain positive powers of the oscillation frequency are considered. Complete asymptotic expansions of fundamental systems of solutions are constructed and substantiated.
@article{ZVMMF_2009_49_12_a4,
     author = {E. V. Krutenko and V. B. Levenshtam},
     title = {Asymptotic analysis of certain systems of linear differential equations with a~large parameter},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {2144--2155},
     year = {2009},
     volume = {49},
     number = {12},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a4/}
}
TY  - JOUR
AU  - E. V. Krutenko
AU  - V. B. Levenshtam
TI  - Asymptotic analysis of certain systems of linear differential equations with a large parameter
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2009
SP  - 2144
EP  - 2155
VL  - 49
IS  - 12
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a4/
LA  - ru
ID  - ZVMMF_2009_49_12_a4
ER  - 
%0 Journal Article
%A E. V. Krutenko
%A V. B. Levenshtam
%T Asymptotic analysis of certain systems of linear differential equations with a large parameter
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2009
%P 2144-2155
%V 49
%N 12
%U http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a4/
%G ru
%F ZVMMF_2009_49_12_a4
E. V. Krutenko; V. B. Levenshtam. Asymptotic analysis of certain systems of linear differential equations with a large parameter. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 12, pp. 2144-2155. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_12_a4/

[1] Liouville J., “Second memoire sur le development des functions en series don divers termes sont assujettis, a satisfaire a une meme eqnation”, J. Math. Pure and Appl., 2 (1837), 16–35

[2] Schlesinger L., “Über asymptotische Darstellungen der Losungen linearer Differential systemabe Funktionen eines Parameter”, Math. Ann., 63 (1907), 207–300

[3] Birkhoff G. D., “Ou the asymptotic character of the solutions of certain linear differential equations containing parameter”, Trans. Amer. Math. Soc., 9 (1908), 219–231 | DOI | MR

[4] Tamarkin Ya. D., O nekotorykh obschikh zadachakh teorii obyknovennykh lineinykh differentsialnykh uravnenii, Petrograd, 1917 | Zbl

[5] Naimark M. A., Lineinye differentsialnye operatory, M., 1954

[6] Koddington E. A., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, Izd-vo inostr. lit., M., 1958

[7] Daletskii Yu. L., “Asimptoticheskie metody dlya nekotorykh differentsialnykh uravnenii s ostsilliruyuschimi koeffitsientami”, Dokl. AN SSSR, 143:5 (1962)

[8] Daletskii Yu. L., Krein M. G., Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nauka, M., 1970 | MR