A Note on the Periodic Solutions for a Class of Third Order Differential Equations

A Note on the Periodic Solutions for a Class of Third Order Differential Equations

The aim of the present work is to study the necessary and sufficient conditions for the existence of periodic solutions for a class of third order differential equations by using the averaging theory. Moreover, we use the symmetry of the Monodromy matrix to study the stability of these solutions.

Bibliographic Details
Main Authors: Zouhair Diab, Juan L. G. Guirao, Juan A. Vera
Format: Article
Language:English
Published: MDPI AG 2021-12-01
Series:Symmetry
Subjects:
differential equations
periodic solution
averaging theory
Online Access:https://www.mdpi.com/2073-8994/13/1/31
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spelling doaj-f6f66d7744ef49fd915daa8c2e040e112020-12-28T00:01:41ZengMDPI AGSymmetry2073-89942021-12-0113313110.3390/sym13010031A Note on the Periodic Solutions for a Class of Third Order Differential EquationsZouhair Diab0Juan L. G. Guirao1Juan A. Vera2Department of Mathematics and Computer Science, Larbi Tebessi University, 12002 Tebessa, AlgeriaDepartamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Hospital de Marina, 30203 Cartagena, Región de Murcia, SpainCentro Universitario de la Defensa, Academia General del Aire, Universidad Politécnica de Cartagena, 30720 Santiago de la Ribera, Región de Murcia, SpainThe aim of the present work is to study the necessary and sufficient conditions for the existence of periodic solutions for a class of third order differential equations by using the averaging theory. Moreover, we use the symmetry of the Monodromy matrix to study the stability of these solutions.https://www.mdpi.com/2073-8994/13/1/31differential equationsperiodic solutionaveraging theory
collection DOAJ
language English
format Article
sources DOAJ
author Zouhair Diab
Juan L. G. Guirao
Juan A. Vera
spellingShingle Zouhair Diab
Juan L. G. Guirao
Juan A. Vera
A Note on the Periodic Solutions for a Class of Third Order Differential Equations
Symmetry
differential equations
periodic solution
averaging theory
author_facet Zouhair Diab
Juan L. G. Guirao
Juan A. Vera
author_sort Zouhair Diab
title A Note on the Periodic Solutions for a Class of Third Order Differential Equations
title_short A Note on the Periodic Solutions for a Class of Third Order Differential Equations
title_full A Note on the Periodic Solutions for a Class of Third Order Differential Equations
title_fullStr A Note on the Periodic Solutions for a Class of Third Order Differential Equations
title_full_unstemmed A Note on the Periodic Solutions for a Class of Third Order Differential Equations
title_sort note on the periodic solutions for a class of third order differential equations
publisher MDPI AG
series Symmetry
issn 2073-8994
publishDate 2021-12-01
description The aim of the present work is to study the necessary and sufficient conditions for the existence of periodic solutions for a class of third order differential equations by using the averaging theory. Moreover, we use the symmetry of the Monodromy matrix to study the stability of these solutions.
topic differential equations
periodic solution
averaging theory
url https://www.mdpi.com/2073-8994/13/1/31
work_keys_str_mv AT zouhairdiab anoteontheperiodicsolutionsforaclassofthirdorderdifferentialequations
AT juanlgguirao anoteontheperiodicsolutionsforaclassofthirdorderdifferentialequations
AT juanavera anoteontheperiodicsolutionsforaclassofthirdorderdifferentialequations
AT zouhairdiab noteontheperiodicsolutionsforaclassofthirdorderdifferentialequations
AT juanlgguirao noteontheperiodicsolutionsforaclassofthirdorderdifferentialequations
AT juanavera noteontheperiodicsolutionsforaclassofthirdorderdifferentialequations
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