Geodesic
Uniform approximation of trajectories maximal to the right under the condition of asymptotic integral stability
Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 211-218 
D. V. Khlopin. Uniform approximation of trajectories maximal to the right under the condition of asymptotic integral stability. Contemporary Mathematics. Fundamental Directions, Proceedings of the International Conference on Mathematical Control Theory and Mechanics (Suzdal, July 3–7, 2009), Tome 42 (2011), pp. 211-218. http://geodesic.mathdoc.fr/item/CMFD_2011_42_a20/
@article{CMFD_2011_42_a20,
     author = {D. V. Khlopin},
     title = {Uniform approximation of trajectories maximal to the right under the condition of asymptotic integral stability},
     journal = {Contemporary Mathematics. Fundamental Directions},
     pages = {211--218},
     year = {2011},
     volume = {42},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CMFD_2011_42_a20/}
}
TY  - JOUR
AU  - D. V. Khlopin
TI  - Uniform approximation of trajectories maximal to the right under the condition of asymptotic integral stability
JO  - Contemporary Mathematics. Fundamental Directions
PY  - 2011
SP  - 211
EP  - 218
VL  - 42
UR  - http://geodesic.mathdoc.fr/item/CMFD_2011_42_a20/
LA  - ru
ID  - CMFD_2011_42_a20
ER  - 
%0 Journal Article
%A D. V. Khlopin
%T Uniform approximation of trajectories maximal to the right under the condition of asymptotic integral stability
%J Contemporary Mathematics. Fundamental Directions
%D 2011
%P 211-218
%V 42
%U http://geodesic.mathdoc.fr/item/CMFD_2011_42_a20/
%G ru
%F CMFD_2011_42_a20

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

The possibility of uniform approximation of solutions maximal to the right is studied in the paper.

[1] Vrkoch I., “Integralnaya ustoichivost”, Chekhoslov. mat. zhurnal, 84:9 (1959), 71–129

[2] Zhukovskii E. S., “O parametricheskom zadanii resheniya differentsialnogo uravneniya i ego priblizhennom postroenii”, Izv. VUZov. Matematika, 1996, no. 4(407), 31–34 | MR | Zbl

[3] Filippov V. V., Fedorchuk V. V., Obschaya topologiya. Osnovnye konstruktsii, Fizmatlit, M., 2006

[4] Khairer E., Nersett S., Vanner G., Reshenie obyknovennykh differentsialnykh uravnenii. Nezhestkie zadachi, Mir, M., 1990 | MR

[5] Shalashilin V. I., Kuznetsov E. B., Metod prodolzheniya po parametru i nailuchshaya parametrizatsiya v prikladnoi matematike i mekhanike, Editorial URSS, M., 1999 | MR

[6] Shtetter Kh., Analiz metodov diskretizatsii dlya obyknovennykh differentsialnykh uravnenii, Mir, M., 1978 | MR

[7] Anderson P., Bernfeld S., “The study of the total stability properties of zero solution of autonomous differential equations under numerical one step methods”, Functional differential equations, 15:2 (2002), 17–31 | MR

[8] Chow S-N., Yorke J. A., “Lyapunov theory and perturbation of stable and asymptotically stable systems”, J. Differential Equations, 15 (1974), 308–321 | DOI | MR | Zbl

[9] Okamura H., “Sur l'unicite des solutions d'un systeme d'equations differentielles ordinaires”, Mem. Coll. Sci. Kyoto Imp. Univ. Ser. A, 23 (1941), 225–231 | Zbl

[10] Viswanath D., “Global errors of numerical ODE solvers and Lyapunov's theory of stability”, IMA J. Numer. Anal., 21:1 (2001), 387–406 | DOI | MR | Zbl