Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales
This paper is concerned with the second-order Hamiltonian system on time scales 𝕋 of the form uΔΔ(ρ(t))+μb(t)|u(t)|μ−2u(t)+∇¯H(t,u(t))=0, Δ-a.e. t∈[0,T]𝕋 , u(0)−u(T)=uΔ(ρ(0))−uΔ(ρ(T))=0, where 0,T∈𝕋. By using the minimax methods in critical theory, an existence th...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2009/328479 |
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| _version_ | 1849407800286904320 |
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| author | You-Hui Su Wan-Tong Li |
| author_facet | You-Hui Su Wan-Tong Li |
| author_sort | You-Hui Su |
| collection | DOAJ |
| description | This paper is concerned with the second-order Hamiltonian system on time scales 𝕋 of the form uΔΔ(ρ(t))+μb(t)|u(t)|μ−2u(t)+∇¯H(t,u(t))=0, Δ-a.e. t∈[0,T]𝕋 , u(0)−u(T)=uΔ(ρ(0))−uΔ(ρ(T))=0, where 0,T∈𝕋. By using the minimax methods in critical theory, an existence theorem of periodic solution for the above system is established. As an application, an example is given to illustrate the result. This is probably the first time the existence of periodic solutions for second-order Hamiltonian system on time scales has been studied by critical theory. |
| format | Article |
| id | doaj-art-43b11df1f76c42e8a55dfa6d08e4b7a2 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-43b11df1f76c42e8a55dfa6d08e4b7a22025-08-20T03:35:57ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2009-01-01200910.1155/2009/328479328479Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time ScalesYou-Hui Su0Wan-Tong Li1School of Mathematics and Physical Sciences, Xuzhou Institute of Technology, Xuzhou, Jiangsu 221008, ChinaSchool of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, ChinaThis paper is concerned with the second-order Hamiltonian system on time scales 𝕋 of the form uΔΔ(ρ(t))+μb(t)|u(t)|μ−2u(t)+∇¯H(t,u(t))=0, Δ-a.e. t∈[0,T]𝕋 , u(0)−u(T)=uΔ(ρ(0))−uΔ(ρ(T))=0, where 0,T∈𝕋. By using the minimax methods in critical theory, an existence theorem of periodic solution for the above system is established. As an application, an example is given to illustrate the result. This is probably the first time the existence of periodic solutions for second-order Hamiltonian system on time scales has been studied by critical theory.http://dx.doi.org/10.1155/2009/328479 |
| spellingShingle | You-Hui Su Wan-Tong Li Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales Discrete Dynamics in Nature and Society |
| title | Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales |
| title_full | Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales |
| title_fullStr | Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales |
| title_full_unstemmed | Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales |
| title_short | Periodic Solution of Second-Order Hamiltonian Systems with a Change Sign Potential on Time Scales |
| title_sort | periodic solution of second order hamiltonian systems with a change sign potential on time scales |
| url | http://dx.doi.org/10.1155/2009/328479 |
| work_keys_str_mv | AT youhuisu periodicsolutionofsecondorderhamiltoniansystemswithachangesignpotentialontimescales AT wantongli periodicsolutionofsecondorderhamiltoniansystemswithachangesignpotentialontimescales |