Geodesic
Periodic solutions of a class of third-order differential equations with two delays depending on time and state
Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 3, pp. 379-399.

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The goal of the present paper is to establish some new results on the existence, uniqueness and stability of periodic solutions for a class of third order functional differential equations with state and time-varying delays. By Krasnoselskii's fixed point theorem, we prove the existence of periodic solutions and under certain sufficient conditions, the Banach contraction principle ensures the uniqueness of this solution. The results obtained in this paper are illustrated by an example.
DOI : 10.14712/1213-7243.2019.018
Classification : 39B12, 39B82
Keywords: periodic solution; iterative differential equation; fixed point theorem; Green's function 
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Khemis, Rabah; Ardjouni, Abdelouaheb; Bouakkaz, Ahlème; Djoudi, Ahcene. Periodic solutions of a class of third-order differential equations with two delays depending on time and state. Commentationes Mathematicae Universitatis Carolinae, Tome 60 (2019) no. 3, pp. 379-399. doi : 10.14712/1213-7243.2019.018. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2019.018/

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