Geodesic
The regularization method for singularly perturbed systems of nonlinear differential equations
Izvestiya. Mathematics, Tome 14 (1980) no. 3, pp. 571-596 
V. F. Safonov. The regularization method for singularly perturbed systems of nonlinear differential equations. Izvestiya. Mathematics, Tome 14 (1980) no. 3, pp. 571-596. http://geodesic.mathdoc.fr/item/IM2_1980_14_3_a3/
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     title = {The regularization method for singularly perturbed systems of nonlinear differential equations},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The singularly perturbed Cauchy problem for systems of ordinary differential equations is studied. A regularized asymptotic solution for this problem is constructed by means of the method developed by S. A. Lomov for a broad class of linear systems and certain nonlinear scalar equations. In the course of constructing the asymptotic solution systems of partial differential equations containing a singularity are considered. For such systems a theory of normal and unique solvability in a class of uniformly convergent exponential series is developed. Asymptotic convergence of formal solutions is studied for the case of purely imaginary eigenvalues of the matrix of the first variation. Bibliography: 16 titles.

[1] Lomov S. A., “Metod vozmuschenii dlya singulyarnykh zadach”, Izv. AN SSSR. Ser. matem., 36 (1972), 635–651 | MR | Zbl

[2] Vasileva A. B., Butuzov V. F., Asimptoticheskie razlozheniya singulyarno vozmuschennykh uravnenii, Nauka, M., 1973 | MR

[3] Kobrin A. I., Martynenko Yu. G., “K zadache postroeniya asimptoticheskogo resheniya kvazilineinykh singulyarno vozmuschennykh uravnenii metodom regulyarizatsii”, Vsesoyuzn. konferentsiya po asimptoticheskim metodam v teorii singulyarnykh vozmuschennykh differentsialnykh i integro-differentsialnykh uravnenii i ikh prilozheniyam, Tezisy dokladov, Frunze, 1975, 322–323

[4] Kobrin A. I., Martynenko Yu. G., Novozhilov I. V., “Primenenie metodov teorii singulyarno vozmuschennykh uravnenii dlya issledovaniya giroskopicheskikh sistem”, Vsesoyuzn. konferentsiya po asimptoticheskim metodam v teorii singulyarnykh vozmuschennykh differentsialnykh i integro-differentsialnykh uravnenii i ikh prilozheniyam, Tezisy dokladov, Frunze, 1975, 321

[5] Lomov S. A., “O skhodimosti asimptoticheskikh ryadov”, Tr. MEI, Issledovaniya po differentsialnym uravneniyam i ikh prilozheniyam, 240, 1975, 91–97 | MR

[6] Lomov S. A., “Matematicheskoe opisanie pogranichnogo sloya v nekotorykh prosteishikh sluchayakh”, Tr. MEI, Issledovaniya po differentsialnym uravneniyam i ikh prilozheniyam, 201, 1974, 79–94 | MR

[7] Safonov V. F., “Regulyarizovannye asimptoticheskie resheniya singulyarno vozmuschennykh sistem so slaboi mnogochlennoi nelineinostyu”, Tr. MEI, Issledovaniya po differentsialnym uravneniyam i ikh prilozheniyam, 201, 1974, 142–150 | MR

[8] Safonov V. F., “Metod regulyarizatsii dlya sistem so slaboi mnogochlennoi nelineinostyu”, Vsesoyuzn. konferentsiya po asimptoticheskim metodam v teorii singulyarnykh vozmuschennykh differentsialnykh i integro-differentsialnykh uravnenii i ikh prilozheniyam, Tezisy dokladov, Frunze, 1975, 314–317

[9] Lomov S. A., “Asimptoticheskie resheniya v kriticheskom sluchae”, Tr. MEI, Matematika, 89, 1971, 3–10 | MR

[10] Konyaev Yu. A., “Postroenie regulyarizovannoi asimptotiki dlya nelineinoi zadachi Koshi”, Vsesoyuzn. konferentsiya po asimptoticheskim metodam v teorii singulyarnykh vozmuschennykh differentsialnykh i integro-differentsialnykh uravnenii i ikh prilozheniyam, Tezisy dokladov, Frunze, 1975, 317–320

[11] Koddington E., Levinson N., Teoriya obyknovennykh differentsialnykh uravnenii, IL, M., 1958

[12] Safonov V. F., “Analiticheskie resheniya odnoi zadachi nelineinoi teorii metoda regulyarizatsii”, Tr. MEI, Elektricheskie sistemy i upravlenie imi, 292, 1976, 103–107 | MR

[13] Dedonne Zh., Osnovy sovremennogo analiza, Mir, M., 1964

[14] Fletto L., Levinson N., “Periodicheskie resheniya singulyarno vozmuschennykh sistem”, Matematika, 2:2 (1958), 61–68

[15] Srubschik L. S., Yudovich V. I., Tezisy dokladov Vsesoyuzn. mezhvuzovskoi konferentsii po primeneniyu metodov funktsionalnogo analiza k resheniyu nelineinykh zadach, Baku, 1965

[16] Khartman F., Obyknovennye differentsialnye uravneniya, Mir, M., 1970 | MR | Zbl