Geodesic
Reduction of the Matier equation to a nonlinear first order one
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 66-69 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

A second order equation with periodic coefficients is considered. It is shown that its analysis can be reduced to the study of a nonlinear equation of the first order. The second approximation is obtained for the first resonance zone of the Mathieu equation describing the behavior of solutions not only inside this zone but also outside it. 
@article{VMUMM_2016_4_a11,
     author = {V. M. Budanov},
     title = {Reduction of the {Matier} equation to a nonlinear first order one},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {66--69},
     year = {2016},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a11/}
}
TY  - JOUR
AU  - V. M. Budanov
TI  - Reduction of the Matier equation to a nonlinear first order one
JO  - Vestnik Moskovskogo universiteta. Matematika, mehanika
PY  - 2016
SP  - 66
EP  - 69
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a11/
LA  - ru
ID  - VMUMM_2016_4_a11
ER  - 
%0 Journal Article
%A V. M. Budanov
%T Reduction of the Matier equation to a nonlinear first order one
%J Vestnik Moskovskogo universiteta. Matematika, mehanika
%D 2016
%P 66-69
%N 4
%U http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a11/
%G ru
%F VMUMM_2016_4_a11
V. M. Budanov. Reduction of the Matier equation to a nonlinear first order one. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 4 (2016), pp. 66-69. http://geodesic.mathdoc.fr/item/VMUMM_2016_4_a11/

[1] Yakubovich V.A., Starzhinskii V.M., Lineinye differentsialnye uravneniya s periodicheskimi koeffitsientami i ikh prilozheniya, Nauka, M., 1972 | MR

[2] Stoker Dzh., Nelineinye kolebaniya v mekhanicheskikh i elektricheskikh sistemakh, IL, M., 1952

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

[4] Zhuravlev V.F., Klimov D.M., Prikladnye metody v teorii kolebanii, Nauka, M., 1988 | MR

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

[6] Kalenova V.I., Morozov V.M., Lineinye nestatsionarnye sistemy i ikh prilozheniya k zadacham mekhaniki, Fizmatlit, M., 2010 | MR

[7] Smolyanskii M.L., Tablitsy neopredelennykh integralov, Nauka, M., 1967

[8] Budanov V.M., “Ob odnoi izokhronnoi nelineinoi sisteme”, Vestn. Mosk. un-ta. Matem. Mekhan., 2013, no. 6, 59–63