Geodesic
On periodic solutions of a second-order ordinary differential equation
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Tome 185 (2020), pp. 13-18.

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

We consider a differential equation containing first- and second-order forms with respect to the phase variable and its derivative with constant coefficients and a periodic inhomogeneity. Using the method of constructing a positively invariant rectangular domain, we examine the existence of a asymptotically stable (in the Lyapunov sense) periodic solution. Criteria for the existence of a periodic solution are formulated in terms of properties of isoclines. We consider cases where the zero isocline is a nondegenerate second-order curve.
Keywords: second-order differential equation, qualitative theory, periodic solution, stability, nonlinear oscillator. 
@article{INTO_2020_185_a1,
     author = {V. V. Abramov and E. Yu. Liskina},
     title = {On periodic solutions of a second-order ordinary differential equation},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {13--18},
     publisher = {mathdoc},
     volume = {185},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2020_185_a1/}
}
TY  - JOUR
AU  - V. V. Abramov
AU  - E. Yu. Liskina
TI  - On periodic solutions of a second-order ordinary differential equation
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2020
SP  - 13
EP  - 18
VL  - 185
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2020_185_a1/
LA  - ru
ID  - INTO_2020_185_a1
ER  - 
%0 Journal Article
%A V. V. Abramov
%A E. Yu. Liskina
%T On periodic solutions of a second-order ordinary differential equation
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2020
%P 13-18
%V 185
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2020_185_a1/
%G ru
%F INTO_2020_185_a1
V. V. Abramov; E. Yu. Liskina. On periodic solutions of a second-order ordinary differential equation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the All-Russian Scientific Conference «Differential Equations and Their Applications» dedicated to the 85th anniversary of Professor M.T.Terekhin. Ryazan State University named for S.A. Yesenin, Ryazan, May 17-18, 2019. Part 1, Tome 185 (2020), pp. 13-18. http://geodesic.mathdoc.fr/item/INTO_2020_185_a1/

[1] Reissig R., Sansone G., Konti R., Kachestvennaya teoriya nelineinykh differentsialnykh uravnenii, Mir, M., 1974

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