On Periodic Solutions of a Second-Order Ordinary Differential Equation

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.

Authors and Affiliations

1. Ryazan State University named for S. A. Yesenin, Ryazan, Russia

   V. V. Abramov & E. Yu. Liskina

Corresponding author

Correspondence to V. V. Abramov.

Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 185, 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, 2020.

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