Geodesic
On some methods for investigating stability
Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 385-402 
Yu. A. Konyaev. On some methods for investigating stability. Sbornik. Mathematics, Tome 192 (2001) no. 3, pp. 385-402. http://geodesic.mathdoc.fr/item/SM_2001_192_3_a3/
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Voir la notice de l'article provenant de la source Math-Net.Ru

This article contains various algorithms for investigating the stability (using the apparatus of the splitting method) of certain classes of non-autonomous systems of linear and quasi-linear ordinary differential equations. The results complement previously known results. Each of the algorithms presented can be regarded (in a certain sense) as a development of the classical method of normal forms, which is very effective in the study of non-linear systems for analysing linear and quasi-linear non-autonomous systems of ordinary differential equations.

[1] Lyapunov A. M., Obschaya zadacha ob ustoichivosti dvizheniya, Gostekhizdat, M.-L., 1935

[2] Demidovich B. P., Lektsii po matematicheskoi teorii ustoichivosti, Nauka, M., 1967 | MR

[3] Bryuno A. D., Lokalnyi metod nelineinogo analiza, Nauka, M., 1979 | MR

[4] Merkin D. R., Vvedenie v teoriyu ustoichivosti dvizheniya, Nauka, M., 1987 | MR | Zbl

[5] Rozo M., Nelineinye kolebaniya i teoriya ustoichivosti, Nauka, M., 1971

[6] Rush N., Abets P., Lalua M., Pryamoi metod Lyapunova v teorii ustoichivosti, Mir, M., 1980 | MR

[7] Lankaster P., Teoriya matrits, Nauka, M., 1978 | MR

[8] Morozov V. M., Kalenova V. I., Otsenivanie i upravlenie v nestatsionarnykh lineinykh sistemakh, Izd-vo MGU, M., 1988

[9] Magnitskii N. A., Asimptoticheskie metody analiza nestatsionarnykh upravlyaemykh sistem, Nauka, M., 1992 | MR

[10] Konyaev Yu. A., “Ob odnom metode issledovaniya nekotorykh zadach teorii vozmuschenii”, Matem. sb., 184:12 (1993), 133–144 | MR | Zbl

[11] Konyaev Yu. A., Martynenko Yu. G., “Ob ustoichivosti statsionarnykh vraschenii simmetrichnogo tverdogo tela v peremennom magnitnom pole”, Prikl. matem. i mekh., 51:3 (1987), 375–381 | MR | Zbl

[12] Konyaev Yu. A., Fedorov Yu. S., “Asimptoticheskii analiz nekotorykh klassov singulyarno vozmuschennykh zadach na poluosi”, Matem. zametki, 62:1 (1997), 111–117 | MR | Zbl

[13] Konyaev Yu. A., Martynenko Yu. G., “Issledovanie ustoichivosti neavtonomnykh sistem differentsialnykh uravnenii kvazipolinomialnogo tipa”, Differents. uravneniya, 34:10 (1999), 1427–1429 | MR

[14] Konyaev Yu. A., “Asimptotika reshenii differentsialnykh uravnenii s polinomialno-periodicheskimi koeffitsientami”, Vestn. MEI, 1996, no. 6, 79–88

[15] Konyaev Yu. A., “Dostatochnye usloviya ustoichivosti reshenii nekotorykh klassov ODU v kriticheskikh sluchayakh”, Differents. uravneniya, 26:4 (1990), 709–712 | MR | Zbl