| 一类二阶非Hamiltonian系统的变分原理及周期解的存在性定理 |
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| 引用本文： | 陈季林.一类二阶非Hamiltonian系统的变分原理及周期解的存在性定理[J].浙江师范大学学报(自然科学版),2008,31(3):275-279. |
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| 作者姓名： | 陈季林 |
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| 作者单位： | 昭通师范高等专科学校数学系,云南昭通657000 |
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| 摘 要： | 研究了阻尼振动问题{ü（t）＋g（t）u（t）=△F（t,u（t））,a.e.t∈0,T]; u（0）-u（T）=u（0）-u（T）=0其中，T＞0,g（t）∈L^∞（0,T,R）,G（t）=∫^tog（s）ds,G（T）=0,F;0,T]×R^N→R，给出了其变分原理和2个周期解的存在性定理，即使在g（t）=0特殊情况下，所得结果也是新的。
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| 关 键 词： | 临界点 周期解 二阶Hamiltonian系统 Sobolev’s不等式 |
Variational principle and existence theorems of periodic solutions for a class of second order non-Hamiltonian systems |
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| CHEN Jilin.Variational principle and existence theorems of periodic solutions for a class of second order non-Hamiltonian systems[J].Journal of Zhejiang Normal University Natural Sciences,2008,31(3):275-279. |
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| Authors: | CHEN Jilin |
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| Institution: | CHEN Jilin (Department of Mathematics, Zhaotong Teacher＇s College, Zhaotong Yunnan 657000, China) |
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| Abstract: | The following damped vibration problem was studied,{ü（t）＋g（t）u（t）=△F（t,u（t））,a.e.t∈0,T]; u（0）-u（T）=u（0）-u（T）=0where T〉0,g（t）∈L^∞（0,T,R）,G（t）=∫^tog（s）ds,G（T）=0,F;0,T]×R^N→R.The variational principle and two existence theorems for periodic solutions were given. In the special case while g（t） = 0 the results presented was also a new result. |
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| Keywords: | critical point periodic solution second order Hamiltonian system Sobolev＇s inequality |
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