Geodesic
Justification of the Averaging Method for Differential Equations with Large Rapidly Oscillating Summands and Boundary Conditions
Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 94-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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The averaging method is justified for normal systems of differential equations with rapidly oscillating summands proportional to the square root of the oscillation frequency in the case of the boundary-value problem on a finite interval and for the problem of bounded solutions on the positive semiaxis with boundary condition at its left endpoint.
Keywords: averaging method, boundary-value problem, problem on the semiaxis, rapidly oscillating summands. 
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V. B. Levenshtam; P. E. Shubin. Justification of the Averaging Method for Differential Equations with Large Rapidly Oscillating Summands and Boundary Conditions. Matematičeskie zametki, Tome 100 (2016) no. 1, pp. 94-108. http://geodesic.mathdoc.fr/item/MZM_2016_100_1_a6/

[1] H. H. Bogolyubov, O nekotorykh statisticheskikh metodakh v matematicheskoi fizike, Izd-vo AN USSR, Lvov, 1945

[2] N. N. Bogolyubov, Yu. A. Mitropolskii, Asimptoticheskie metody v teorii nelineinykh kolebanii, Nauka, M., 1974 | MR | Zbl

[3] S. K. Godunov, Obyknovennye differentsialnye uravneniya s postoyannymi koeffitsientami, T. 1, Izd-vo Novosibirsk. un-ta, Novosibirsk, 1994 | MR | Zbl

[4] V. B. Levenshtam, “Asimptoticheskoe integrirovanie differentsialnykh uravnenii, soderzhaschikh bystro ostsilliruyuschie slagaemye s bolshimi amplitudami. I”, Differents. uravneniya, 41:6 (2005), 761–770 | Zbl

[5] V. B. Levenshtam, “Asimptoticheskoe integrirovanie differentsialnykh uravnenii, soderzhaschikh bystro ostsilliruyuschie slagaemye s bolshimi amplitudami. II”, Differents. uravneniya, 41:8 (2005), 1084–1091 | Zbl

[6] V. B. Levenshtam, “Asimptoticheskoe integrirovanie differentsialnykh uravnenii s bolshimi vysokochastotnymi slagaemymi”, Dokl. RAN, 405:2 (2005), 169–172 | Zbl

[7] V. B. Levenshtam, G. L. Khatlamadzhiyan, “Rasprostranenie teorii usredneniya na differentsialnye uravneniya, soderzhaschie bystro ostsilliruyuschie slagaemye s bolshimi amplitudami. Zadacha o periodicheskikh resheniyakh”, Izv. vuzov. Matem., 2006, no. 6, 35–47 | MR | Zbl

[8] V. I. Yudovich, “Vibrodinamika sistem so svyazyami”, Dokl. RAN, 354:2 (1997), 622–624 | Zbl

[9] V. I. Yudovich, “Vibrodinamika i vibrogeometriya mekhanicheskikh sistem so svyazyami”, Usp. mekh., 4:3 (2006), 26–158

[10] V. B. Levenshtam, P. E. Shubin, “Averaging of evolution system with boundary conditions”, Sci. Publ. of the State Univ. of Novi Pazar Ser. A: Appl. Math., Inform. and Mech., 5:2 (2013), 61–67

[11] V. B. Levenshtam, P. E. Shubin, “Justification of the averaging method for the boundary value problems on a finite or semi-infinite interval”, Sci. Publ. of the State Univ. of Novi Pazar Ser. A: Appl. Math., Inform. and Mech., 7:2 (2015), 81–89 | DOI

[12] Yu. L. Daletskii, M. G. Krein, Ustoichivost reshenii differentsialnykh uravnenii v banakhovom prostranstve, Nelineinyi analiz i ego prilozheniya, Nauka, M., 1970 | MR | Zbl

[13] I. B. Simonenko, “Obosnovanie metoda osredneniya dlya abstraktnykh parabolicheskikh uravnenii”, Matem. sb., 81 (123):1 (1970), 53–61 | MR | Zbl

[14] M. A. Krasnoselskii, V. Sh. Burd, Yu. S. Kolesov, Nelineinye pochti periodicheskie kolebaniya, Nauka, M., 1970 | MR | Zbl