A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type

In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type [Formula: see text] where [Formula: see text] is singular at [Formula: see text] , φ and h are T-periodic functions. By using the continuation...

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Detalles Bibliográficos
Autor principal: Lu, Shiping
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2017
Materias:
Research
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5306233/
https://www.ncbi.nlm.nih.gov/pubmed/28239242
http://dx.doi.org/10.1186/s13660-016-1285-8
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author Lu, Shiping
author_facet Lu, Shiping
author_sort Lu, Shiping
collection PubMed
description In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type [Formula: see text] where [Formula: see text] is singular at [Formula: see text] , φ and h are T-periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained. It is interesting that the sign of the function [Formula: see text] is allowed to change for [Formula: see text] .
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spelling pubmed-53062332017-02-24 A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type Lu, Shiping J Inequal Appl Research In this paper, the problem of the existence of a periodic solution is studied for the second order differential equation with a singularity of repulsive type [Formula: see text] where [Formula: see text] is singular at [Formula: see text] , φ and h are T-periodic functions. By using the continuation theorem of Manásevich and Mawhin, a new result on the existence of positive periodic solution is obtained. It is interesting that the sign of the function [Formula: see text] is allowed to change for [Formula: see text] . Springer International Publishing 2017-02-07 2017 /pmc/articles/PMC5306233/ /pubmed/28239242 http://dx.doi.org/10.1186/s13660-016-1285-8 Text en © The Author(s) 2017 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Research
Lu, Shiping
A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type
title A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type
title_full A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type
title_fullStr A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type
title_full_unstemmed A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type
title_short A new result on the existence of periodic solutions for Liénard equations with a singularity of repulsive type
title_sort new result on the existence of periodic solutions for liénard equations with a singularity of repulsive type
topic Research
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5306233/
https://www.ncbi.nlm.nih.gov/pubmed/28239242
http://dx.doi.org/10.1186/s13660-016-1285-8
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