Rotating periodic solutions for second order systems with Hartman-type nonlinearity

Rotating periodic solutions for second order systems with Hartman-type nonlinearity

Abstract In this paper, by a constructive proof based on the homotopy continuation method, we prove that the second order system x″=g(t,x) $x''=g(t,x)$ admits rotating periodic solutions with form u(t+T)=Qu(t) $u(t+T)=Qu(t)$ for any orthogonal matrix Q when the nonlinearity g admits the Ha...

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Main Authors: Jian Li, Xiaojun Chang, Yong Li
Format: Article
Language:English
Published: SpringerOpen 2018-03-01
Series:Boundary Value Problems
Subjects:
Rotating periodic solutions
Second order systems
Hartman-type nonlinearity
Homotopy continuation method
Online Access:http://link.springer.com/article/10.1186/s13661-018-0955-5
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spelling doaj-5619a9a4351e4df8abfca7610ec84f132020-11-25T02:10:08ZengSpringerOpenBoundary Value Problems1687-27702018-03-012018111110.1186/s13661-018-0955-5Rotating periodic solutions for second order systems with Hartman-type nonlinearityJian Li0Xiaojun Chang1Yong Li2School of Mathematics and Statistics & Center for Mathematics and Interdisciplinary Sciences, Northeast Normal UniversitySchool of Mathematics and Statistics & Center for Mathematics and Interdisciplinary Sciences, Northeast Normal UniversitySchool of Mathematics and Statistics & Center for Mathematics and Interdisciplinary Sciences, Northeast Normal UniversityAbstract In this paper, by a constructive proof based on the homotopy continuation method, we prove that the second order system x″=g(t,x) $x''=g(t,x)$ admits rotating periodic solutions with form u(t+T)=Qu(t) $u(t+T)=Qu(t)$ for any orthogonal matrix Q when the nonlinearity g admits the Hartman-type condition.http://link.springer.com/article/10.1186/s13661-018-0955-5Rotating periodic solutionsSecond order systemsHartman-type nonlinearityHomotopy continuation method
collection DOAJ
language English
format Article
sources DOAJ
author Jian Li
Xiaojun Chang
Yong Li
spellingShingle Jian Li
Xiaojun Chang
Yong Li
Rotating periodic solutions for second order systems with Hartman-type nonlinearity
Boundary Value Problems
Rotating periodic solutions
Second order systems
Hartman-type nonlinearity
Homotopy continuation method
author_facet Jian Li
Xiaojun Chang
Yong Li
author_sort Jian Li
title Rotating periodic solutions for second order systems with Hartman-type nonlinearity
title_short Rotating periodic solutions for second order systems with Hartman-type nonlinearity
title_full Rotating periodic solutions for second order systems with Hartman-type nonlinearity
title_fullStr Rotating periodic solutions for second order systems with Hartman-type nonlinearity
title_full_unstemmed Rotating periodic solutions for second order systems with Hartman-type nonlinearity
title_sort rotating periodic solutions for second order systems with hartman-type nonlinearity
publisher SpringerOpen
series Boundary Value Problems
issn 1687-2770
publishDate 2018-03-01
description Abstract In this paper, by a constructive proof based on the homotopy continuation method, we prove that the second order system x″=g(t,x) $x''=g(t,x)$ admits rotating periodic solutions with form u(t+T)=Qu(t) $u(t+T)=Qu(t)$ for any orthogonal matrix Q when the nonlinearity g admits the Hartman-type condition.
topic Rotating periodic solutions
Second order systems
Hartman-type nonlinearity
Homotopy continuation method
url http://link.springer.com/article/10.1186/s13661-018-0955-5
work_keys_str_mv AT jianli rotatingperiodicsolutionsforsecondordersystemswithhartmantypenonlinearity
AT xiaojunchang rotatingperiodicsolutionsforsecondordersystemswithhartmantypenonlinearity
AT yongli rotatingperiodicsolutionsforsecondordersystemswithhartmantypenonlinearity
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