Rabah Khemis, Abdelouaheb Ardjouni, Ahlème Bouakkaz, Ahcene Djoudi
Periodic solutions of a class of third-order differential equations with two delays depending on time and state

Comment.Math.Univ.Carolin. 60,3 (2019) 379-399.

Abstract: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.

Keywords: periodic solution; iterative differential equation; fixed point theorem; Green's function

DOI: DOI 10.14712/1213-7243.2019.018
AMS Subject Classification: 39B12 39B82