Geodesic
A new approach to the question of existence of periodic solutions
Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1077-1107

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This paper is devoted to a new type of sufficient conditions for the existence of periodic solutions of ordinary differential equations and functional differential equations of point type. These conditions are based on the use of asymptotic properties of solutions of differential equations that have not been used in the study of periodic solutions because of considerations restricting such equations to an interval equal to the period.
Keywords: differential equations, periodic solutions. 
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     author = {L. A. Beklaryan},
     title = {A new approach to the question of existence of periodic solutions},
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L. A. Beklaryan. A new approach to the question of existence of periodic solutions. Izvestiya. Mathematics , Tome 82 (2018) no. 6, pp. 1077-1107. http://geodesic.mathdoc.fr/item/IM2_2018_82_6_a0/