Geodesic
Coincidence of linear approximation classes providing asymptotic and particular instabilities
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2024), pp. 16-21 
A.A. Bondarev. Coincidence of linear approximation classes providing asymptotic and particular instabilities. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2024), pp. 16-21. http://geodesic.mathdoc.fr/item/VMUMM_2024_5_a1/
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     title = {Coincidence of linear approximation classes providing asymptotic and particular instabilities},
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Voir la notice de l'article provenant de la source Math-Net.Ru

A coincidence of classes to linear approximations that provide the properties of asymptotic and particular instabilities (of three types separately: Lyapunov, Perron, and upper-limit) of the zero solution to a non-one-dimensional differential system is proved.

[1] Lyapunov A.M., Obschaya zadacha ob ustoichivosti dvizheniya, GITTL, M.–L., 1950

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

[3] Sergeev I.N., “Opredelenie ustoichivosti po Perronu i ee svyaz s ustoichivostyu po Lyapunovu”, Differents. uravneniya, 54:6 (2018), 855–856

[4] Sergeev I.N., “Opredelenie verkhnepredelnoi ustoichivosti i ee svyaz s ustoichivostyu po Lyapunovu i ustoichivostyu po Perronu”, Differents. uravneniya, 56:11 (2020), 1556–1557

[5] Sergeev I.N., “Klassy lineinykh priblizhenii, obespechivayuschikh razlichnye vidy ustoichivosti ili neustoichivosti differentsialnykh sistem”, Vestn. Mosk. un-ta. Matem. Mekhan., 2023, no. 4, 8–15 | DOI

[6] Sergeev I.N., “O perronovskikh, lyapunovskikh i verkhnepredelnykh svoistvakh ustoichivosti differentsialnykh sistem”, Tr. seminara im. I.G. Petrovskogo, 33, 2023, 353–423

[7] Sergeev I.N., Lektsii po differentsialnym uravneniyam, M., 2019

[8] Bondarev A.A., “Primer polnoi, no ne globalnoi neustoichivosti po Perronu”, Vestn. Mosk. un-ta. Matem. Mekhan., 2021, no. 2, 43–47

[9] Bondarev A.A., “Primer differentsialnoi sistemy s perronovskoi i verkhnepredelnoi polnoi neustoichivostyu, no massivnoi chastnoi ustoichivostyu”, Differents. uravneniya, 58:2 (2022), 147–152

[10] Bondarev A.A., “O suschestvovanii differentsialnoi sistemy s lyapunovskoi globalnoi neustoichivostyu, vse resheniya kotoroi stremyatsya k nulyu pri neogranichennom roste vremeni”, Differents. uravneniya, 58:8 (2022), 1011–1019

[11] Bondarev A.A., “An example of contrasting combination to stability and instability properties in even-dimensional spaces”, Mem. Diff. Equations and Math. Phys., 87 (2022), 25–36

[12] Bondarev A.A., Sergeev I.N., “Primery differentsialnykh sistem s kontrastnymi sochetaniyami lyapunovskikh, perronovskikh i verkhnepredelnykh svoistv”, Dokl. RAN. Matematika, informatika, protsessy upravleniya, 506 (2022), 25–29

[13] Bondarev A.A., “Dva kontrastnykh primera mnogomernykh differentsialnykh sistem s lyapunovskoi krainei neustoichivostyu”, Matem. zametki, 115:1 (2024), 24–42 | DOI