Geodesic
On the Majorant Method for the Cauchy--Kovalevskaya Problem
Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 363-374.

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

We present a theory which allows us to justify the existence theorems and derive majorant estimates for solutions of the Cauchy problem for a countable system of partial differential equations. Our results also allow to estimate the maximum existence interval for a solution. 
@article{MZM_2001_69_3_a5,
     author = {O. \`E. Zubelevich},
     title = {On the {Majorant} {Method} for the {Cauchy--Kovalevskaya} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {363--374},
     publisher = {mathdoc},
     volume = {69},
     number = {3},
     year = {2001},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a5/}
}
TY  - JOUR
AU  - O. È. Zubelevich
TI  - On the Majorant Method for the Cauchy--Kovalevskaya Problem
JO  - Matematičeskie zametki
PY  - 2001
SP  - 363
EP  - 374
VL  - 69
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a5/
LA  - ru
ID  - MZM_2001_69_3_a5
ER  - 
%0 Journal Article
%A O. È. Zubelevich
%T On the Majorant Method for the Cauchy--Kovalevskaya Problem
%J Matematičeskie zametki
%D 2001
%P 363-374
%V 69
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a5/
%G ru
%F MZM_2001_69_3_a5
O. È. Zubelevich. On the Majorant Method for the Cauchy--Kovalevskaya Problem. Matematičeskie zametki, Tome 69 (2001) no. 3, pp. 363-374. http://geodesic.mathdoc.fr/item/MZM_2001_69_3_a5/

[1] Klein F., Lektsii o razvitii matematiki v XIX stoletii, T. 1, Nauka, M., 1989 | Zbl

[2] Kochina P. Ya., Sofya Vasilevna Kovalevskaya, Nauka, M., 1981

[3] Nirenberg L., Lektsii po nelineinomu funktsionalnomu analizu, Mir, M., 1977

[4] Safonov M. V., “The abstract Cauchy–Kovalevskaya theorem in a weighted Banach space”, Comm. Pure Appl. Math., 48 (1995), 629–643 | DOI | MR

[5] Treschev D. V., Vvedenie v teoriyu vozmuschenii gamiltonovykh sistem, Fazis, M., 1998

[6] Pronin A., Treschev D., “Continuous averaging in multi-freqncy slow-fast systems”, Regular and Chaotic Dynamics, 5:2 (2000), 157–170 | DOI | MR | Zbl

[7] Lednev N. A., “Novyi metod resheniya differentsialnykh uravnenii s chastnymi proizvodnymi”, Matem. sb., 22 (64):2 (1948), 205–266 | MR | Zbl

[8] Shvarts L., Analiz, T. 2, Mir, M., 1972

[9] Fikhtengolts G. M., Kurs differentsialnogo i integralnogo ischisleniya, T. 3, Fizmatgiz, M., 1960

[10] Smirnov V. I., Kurs vysshei matematiki, T. 5, GIFML, M., 1959