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

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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. 
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     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},
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     publisher = {mathdoc},
     volume = {185},
     year = {2020},
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     url = {http://geodesic.mathdoc.fr/item/INTO_2020_185_a1/}
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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/