Geodesic
On branching of periodic solutions of quasilinear systems of ordinary differential equations
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 3-10.

Voir la notice de l'article provenant de la source Math-Net.Ru

In this paper, a normal system of ordinary differential equations with a small parameter is examined. We obtain conditions for the existence and stability of a periodic solution, which, at the zero value of the parameter, satisfies a linear homogeneous system. The reasoning is based on the analysis of properties of the monodromy operator.
Keywords: differential equation, periodic solution, small parameter, monodromy operator. 
@article{INTO_2022_217_a0,
     author = {V. V. Abramov and E. Yu. Liskina},
     title = {On branching of periodic solutions of quasilinear systems of ordinary differential equations},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--10},
     publisher = {mathdoc},
     volume = {217},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2022_217_a0/}
}
TY  - JOUR
AU  - V. V. Abramov
AU  - E. Yu. Liskina
TI  - On branching of periodic solutions of quasilinear systems of ordinary differential equations
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2022
SP  - 3
EP  - 10
VL  - 217
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2022_217_a0/
LA  - ru
ID  - INTO_2022_217_a0
ER  - 
%0 Journal Article
%A V. V. Abramov
%A E. Yu. Liskina
%T On branching of periodic solutions of quasilinear systems of ordinary differential equations
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2022
%P 3-10
%V 217
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2022_217_a0/
%G ru
%F INTO_2022_217_a0
V. V. Abramov; E. Yu. Liskina. On branching of periodic solutions of quasilinear systems of ordinary differential equations. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Algebra, geometry, differential equations, Tome 217 (2022), pp. 3-10. http://geodesic.mathdoc.fr/item/INTO_2022_217_a0/

[1] Abramov V. V., “Ustoichivost malogo periodicheskogo resheniya”, Vestn. RAEN., 13:4 (2013), 3–5

[2] Abramov V. V., “K zadache ob ustoichivosti malogo periodicheskogo resheniya”, Itogi nauki tekhn. Sovr. mat. prilozh. Temat. obz., 148 (2018), 3–9

[3] Grebenikov E. A., Ryabov Yu. A., Konstruktivnye metody analiza nelineinykh sistem, Nauka, M., 1979 | MR

[4] Liskina E. Yu., Nenulevye periodicheskie resheniya sistem obyknovennykh differentsialnykh uravnenii, Avtoref. diss. na soisk. uch. step. kand. fiz.-matyu nauk, MGU im. N. P. Ogareva, Saransk, 2000

[5] Liskina E. Yu., “O periodicheskom reshenii spetsialnogo vida sistemy obyknovennykh differentsialnykh uravnenii”, Vestn. Tambov. un-ta. Ser. Estestv. tekhn. nauki., 5:4 (2000), 472–473

[6] Krasnoselskii M. A., Operator sdviga po traektoriyam differentsialnykh uravnenii, Nauka, M., 1966 | MR

[7] Malkin I. G., Nekotorye zadachi teorii nelineinykh kolebanii, GITTL, M., 1956

[8] Khorn R. A., Dzhonson Ch. R., Matrichnyi analiz, Mir, M., 1989 | MR