Periodic solutions of a class of third-order differential equations with two delays depending on time and state

Rabah Khemis; Abdelouaheb Ardjouni; Ahlème Bouakkaz; Ahcene Djoudi

Commentationes Mathematicae Universitatis Carolinae (2019)

  • Volume: 60, Issue: 3, page 379-399
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Khemis, Rabah, et al. "Periodic solutions of a class of third-order differential equations with two delays depending on time and state." Commentationes Mathematicae Universitatis Carolinae 60.3 (2019): 379-399. <http://eudml.org/doc/294223>.

@article{Khemis2019,
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.},
author = {Khemis, Rabah, Ardjouni, Abdelouaheb, Bouakkaz, Ahlème, Djoudi, Ahcene},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {periodic solution; iterative differential equation; fixed point theorem; Green's function},
language = {eng},
number = {3},
pages = {379-399},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Periodic solutions of a class of third-order differential equations with two delays depending on time and state},
url = {http://eudml.org/doc/294223},
volume = {60},
year = {2019},
}

TY - JOUR
AU - Khemis, Rabah
AU - Ardjouni, Abdelouaheb
AU - Bouakkaz, Ahlème
AU - Djoudi, Ahcene
TI - Periodic solutions of a class of third-order differential equations with two delays depending on time and state
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2019
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 60
IS - 3
SP - 379
EP - 399
AB - 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.
LA - eng
KW - periodic solution; iterative differential equation; fixed point theorem; Green's function
UR - http://eudml.org/doc/294223
ER -

References

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