Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system

Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system

In this article, we study the existence of non-zero periodic solutions for Hamiltonian systems with impulsive conditions. By using a variational method and a variant fountain theorem, we obtain new criteria to guarantee that the system has at least one non-zero periodic solution or infinitely m...

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Bibliographic Details
Main Authors: Dan Zhang, Qinghua Wu, Binxiang Dai
Format: Article
Language:English
Published: Texas State University 2014-05-01
Series:Electronic Journal of Differential Equations
Subjects:
Impulsive differential equations
critical point theory
periodic solution
variant fountain theorems
Online Access:http://ejde.math.txstate.edu/Volumes/2014/121/abstr.html
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spelling doaj-d5287e7d14f148d685bbc3998e89266a2020-11-24T23:54:33ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912014-05-012014121,112Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian systemDan Zhang0Qinghua Wu1Binxiang Dai2 Hunan Univ. of Science and Engineering, Yongzhou, China Hunan Univ. of Science and Engineering, Yongzhou, China Central South Univ., Changsha, Hunan, China In this article, we study the existence of non-zero periodic solutions for Hamiltonian systems with impulsive conditions. By using a variational method and a variant fountain theorem, we obtain new criteria to guarantee that the system has at least one non-zero periodic solution or infinitely many non-zero periodic solutions. However, without impulses, there is no non-zero periodic solution for the system under our conditions.http://ejde.math.txstate.edu/Volumes/2014/121/abstr.htmlImpulsive differential equationscritical point theoryperiodic solutionvariant fountain theorems
collection DOAJ
language English
format Article
sources DOAJ
author Dan Zhang
Qinghua Wu
Binxiang Dai
spellingShingle Dan Zhang
Qinghua Wu
Binxiang Dai
Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
Electronic Journal of Differential Equations
Impulsive differential equations
critical point theory
periodic solution
variant fountain theorems
author_facet Dan Zhang
Qinghua Wu
Binxiang Dai
author_sort Dan Zhang
title Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
title_short Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
title_full Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
title_fullStr Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
title_full_unstemmed Existence and multiplicity of periodic solutions generated by impulses for second-order Hamiltonian system
title_sort existence and multiplicity of periodic solutions generated by impulses for second-order hamiltonian system
publisher Texas State University
series Electronic Journal of Differential Equations
issn 1072-6691
publishDate 2014-05-01
description In this article, we study the existence of non-zero periodic solutions for Hamiltonian systems with impulsive conditions. By using a variational method and a variant fountain theorem, we obtain new criteria to guarantee that the system has at least one non-zero periodic solution or infinitely many non-zero periodic solutions. However, without impulses, there is no non-zero periodic solution for the system under our conditions.
topic Impulsive differential equations
critical point theory
periodic solution
variant fountain theorems
url http://ejde.math.txstate.edu/Volumes/2014/121/abstr.html
work_keys_str_mv AT danzhang existenceandmultiplicityofperiodicsolutionsgeneratedbyimpulsesforsecondorderhamiltoniansystem
AT qinghuawu existenceandmultiplicityofperiodicsolutionsgeneratedbyimpulsesforsecondorderhamiltoniansystem
AT binxiangdai existenceandmultiplicityofperiodicsolutionsgeneratedbyimpulsesforsecondorderhamiltoniansystem
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