Geodesic
Asymptotics of the solution to a differential equation with a small parameter in the case of two limit solutions
Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 98-108 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The asymptotics of an initial value problem with a small parameter is studied. 
@article{TIMM_2006_12_1_a8,
     author = {A. M. Il'in and S. F. Dolbeeva},
     title = {Asymptotics of the solution to a~differential equation with a~small parameter in the case of two limit solutions},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {98--108},
     year = {2006},
     volume = {12},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a8/}
}
TY  - JOUR
AU  - A. M. Il'in
AU  - S. F. Dolbeeva
TI  - Asymptotics of the solution to a differential equation with a small parameter in the case of two limit solutions
JO  - Trudy Instituta matematiki i mehaniki
PY  - 2006
SP  - 98
EP  - 108
VL  - 12
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a8/
LA  - ru
ID  - TIMM_2006_12_1_a8
ER  - 
%0 Journal Article
%A A. M. Il'in
%A S. F. Dolbeeva
%T Asymptotics of the solution to a differential equation with a small parameter in the case of two limit solutions
%J Trudy Instituta matematiki i mehaniki
%D 2006
%P 98-108
%V 12
%N 1
%U http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a8/
%G ru
%F TIMM_2006_12_1_a8
A. M. Il'in; S. F. Dolbeeva. Asymptotics of the solution to a differential equation with a small parameter in the case of two limit solutions. Trudy Instituta matematiki i mehaniki, Dynamical systems: modeling, optimization, and control, Tome 12 (2006) no. 1, pp. 98-108. http://geodesic.mathdoc.fr/item/TIMM_2006_12_1_a8/

[1] Vasileva A. B., Butuzov V. F., Asimptoticheskie metody v teorii singulyarnykh vozmuschenii, Vyssh. shk., M., 1990 | MR

[2] Lebovitz N. R., Schaar R. J., “Exchange of stabilities in autonomous systems”, Studies in Appl. Math., 54:3 (1975), 229–260 | MR | Zbl

[3] Lebovitz N. R., Schaar R. J., “Exchange of stabilities in autonomous systems. II. Vertical bifurcation”, Studies in Appl. Math., 56:1 (1977), 1–50 | MR | Zbl

[4] Nefedov N., Schneider K., Singularly perturbed systems: Case of exchange of stability, Preprint No 158, Weierstrass-Institut für Angewandte Analysis und Stochastik, Berlin, 1995

[5] Butuzov V., Nefedov N., Schneider K., Singularly perturbed boundary value problems for systems of Tichonov's type in case of exchange of stabilities. Weierstrass-Institut für Angewandte Analysis und Stochastik, Preprint No 408, Berlin, 1998

[6] Butuzov V. F., Nefedov N. N., “Singulyarno vozmuschennaya kraevaya zadacha dlya uravneniya vtorogo poryadka v sluchae smeny ustoichivosti”, Mat. zametki, 63:3 (1998), 354–362 | MR | Zbl

[7] Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989, 336 pp. | MR

[8] Dolbeeva S. F., Ilin A. M., “Asimptotika resheniya differentsialnogo uravneniya s malym parametrom pri uslovii peresecheniya linii ustoichivosti predelnogo resheniya”, Dokl. Akademii Nauk, 408:4 (2006), 443–445 | MR

[9] Kamke E., Spravochnik po obyknovennym differentsialnym uravneniyam, IL, M., 1951, 828 pp.

[10] Zaitsev V. F., Polyanin A. D., Spravochnik po obyknovennym differentsialnym uravneniyam, Nauka, M., 1995, 560 pp. | MR