Asymptotic behavior of solutions to a Cauchy problem with a turning point in the case of change of stability
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 103-105.

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We prove the existence of solutions to a perturbed Cauchy problem on an infinite interval and obtain asymptotic estimates of the proximity of solutions to the perturbed and nonperturbed problems on an infinite interval containing an unstable interval.
Keywords: singularly perturbed Cauchy problem, asymptotic stability, asymptotics, small parameter, turning point, unstable interval.
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E. A. Tursunov. Asymptotic behavior of solutions to a Cauchy problem with a turning point in the case of change of stability. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Mathematical Analysis, Tome 156 (2018), pp. 103-105. http://geodesic.mathdoc.fr/item/INTO_2018_156_a8/

[1] Neishtadt A. I., “Asimptoticheskoe issledovanie poteri ustoichivosti ravnovesiya pri medlennom prokhozhdenii pary sobstvennykh chisel cherez mnimuyu os”, Usp. mat. nauk, 40:5 (1985), 300–301

[2] Neishtadt A. I., Sidorenko V. V., Zapazdyvanie poteri ustoichivosti v sisteme Tsiglera, IPM RAN im. M. V. Keldysha, M., 1995

[3] Neishtadt A. I., “O zatyagivanii poteri ustoichivosti pri dinamicheskikh bifurkatsiyakh, I”, Differ. uravn., 23:12 (1987), 2060–2067 | MR

[4] Neishtadt A. I., “O zatyagivanii poteri ustoichivosti pri dinamicheskikh bifurkatsiyakh, II”, Differ. uravn., 24:2 (1988), 226–233 | MR

[5] Tikhonov A. N., “Sistemy differentsialnykh uravnenii, soderzhaschie malye parametry pri proizvodnykh”, Mat. sb., 31 (73):3 (1952), 575–586 | Zbl

[6] Tursunov D. A., Asimptoticheskoe povedenie resheniya singulyarno vozmuschennykh zadach v sluchae smeny ustoichivosti, kogda sobstvennye znacheniya imeyut $n$-kratnyi polyus, Diss. na soisk. uch. step. kand. fiz.-mat. nauk, Osh, 2005

[7] Fedoryuk M. V., Metod perevala, Librokom, M., 2010

[8] Fedoryuk M. V., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983

[9] Shishkova M. A., “Rassmotrenie odnoi sistemy differentsialnykh uravnenii s malym parametrom pri vysshikh proizvodnykh”, Dokl. AN SSSR, 209:3 (1973), 576–579 | MR | Zbl

[10] Wasow W., Asymptotic expansions for ordinary differential equations, Dover, New York, 1965 | MR