Research of the nonautonomous system of ODE by the ideas of the method of guiding functions
Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 510-516 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We indicate sufficient conditions connected with the method of guiding functions, under which periodically perturbed autonomous system of ODE has an periodic solution.
Keywords: periodically perturbed autonomous system of ODE, topological degree of transformation, Steclov average, coercitivity of transformation.
@article{VTAMU_2018_23_123_a20,
     author = {A. I. Perov and V. K. Kaverina},
     title = {Research of the nonautonomous system of {ODE} by the ideas of the method of guiding functions},
     journal = {Vestnik rossijskih universitetov. Matematika},
     pages = {510--516},
     year = {2018},
     volume = {23},
     number = {123},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a20/}
}
TY  - JOUR
AU  - A. I. Perov
AU  - V. K. Kaverina
TI  - Research of the nonautonomous system of ODE by the ideas of the method of guiding functions
JO  - Vestnik rossijskih universitetov. Matematika
PY  - 2018
SP  - 510
EP  - 516
VL  - 23
IS  - 123
UR  - http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a20/
LA  - ru
ID  - VTAMU_2018_23_123_a20
ER  - 
%0 Journal Article
%A A. I. Perov
%A V. K. Kaverina
%T Research of the nonautonomous system of ODE by the ideas of the method of guiding functions
%J Vestnik rossijskih universitetov. Matematika
%D 2018
%P 510-516
%V 23
%N 123
%U http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a20/
%G ru
%F VTAMU_2018_23_123_a20
A. I. Perov; V. K. Kaverina. Research of the nonautonomous system of ODE by the ideas of the method of guiding functions. Vestnik rossijskih universitetov. Matematika, Tome 23 (2018) no. 123, pp. 510-516. http://geodesic.mathdoc.fr/item/VTAMU_2018_23_123_a20/

[1] N. N. Krasovskiy, Some Problems of \linebreak Dynamic Stability Theory, Fizmatgiz Publ., Moscow, 1959, 211 pp. (In Russian)

[2] M. A. Krasnoselskiy, The Shift Operator on the Path of the Differential Equations, Nauka Publ., Moscow, 1960, 331 pp. (In Russian) | MR

[3] V. G. Zvyagin, The Introduction in the Topological Methods of Analysis, Voronezh State University Publishing House, Voronezh, 2014, 290 pp. (In Russian)

[4] G. Ortega, V. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Mir Publ., Moscow, 1979, 558 pp. (In Russian)

[5] A. I. Perov, V. K. Evchenko, Method of Guiding Functions, Publ.-Polygraphic Centre of Voronezh State University, Voronezh, 2012, 182 pp. (In Russian)

[6] I. P. Natanson, Theory of Functions of Real Variable, Nauka Publ., Moscow, 1974, 480 pp. (In Russian) | MR

[7] R. Reissig, G. Sansone, R. Conti, Qualitative Theory of Nonlinear Differential Equations, Nauka Publ., Moscow, 1970, 318 pp. (In Russian)

[8] G. Sansone, Ordinary Differential Equations, v. 2, Foreign Languages Publishing House, Moscow, 1954, 346 pp. (In Russian)

[9] V. I. Zubov, The Theory of Oscillations, Vysshaya Shkola Publ., Moscow, 1979, 400 pp. (In Russian)

[10] V. K. Evchenko, “About one problem from the oscillations theory”, Tambov University Reports. Series: Natural and Technical Sciences, 20:5 (2015), 1136–1137 (In Russian)