Geodesic
Periodic solutions of a differential equation with relay nonlinearity with delay
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 3-12.

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For one class of second-order differential equations with relay nonlinearity and delay, orbitally stable periodic solutions are found by means of the recurrence operator, which is a suspension over some one-dimensional mapping. The analysis of this one-dimensional mapping shows that there exist domains of parameters for which exponentially orbitally stable periodic solutions exist.
Keywords: differential equation with delay, recurrence operator, stability 
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D. D. Bain. Periodic solutions of a differential equation with relay nonlinearity with delay. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the Voronezh international spring mathematical school "Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV", Voronezh, May 3-9, 2023, Part 2, Tome 231 (2024), pp. 3-12. http://geodesic.mathdoc.fr/item/INTO_2024_231_a0/

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