平面奇异Hamilton系统的同宿轨道
Homoclinic Orbits for a Singular Second Order Planar Hamiltonian System
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摘要: 用变分方法证明了二阶奇异平面哈密顿系统的同宿轨道的存在性.同宿轨道存在的主要条件是奇异势 能函数满足强力条件和有唯一最大值.逼近问题的相应泛函满足PS紧性条件,到达其下确界,从而得到逼近问 题的解.所求的同宿轨道就是这些解的极限.
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关键词:
- 临界点 /
- 奇异Hamilton系统 /
- 同宿轨道
Abstract: The existence of a homoclinic orbit for a singular second order planarHamiltonian system is proved by using variational methods. The main assumptions are the strong force condition and the uniqueness of a global maximum of a singular potential. The functional corresponding to the approximate problem satisfies the Palais-Smale compactness condition and attains its infimum. Solutions of this approximate problem are obtained as minimal points of the fanctional. The homoclinic orbit is the limit of these solutions.-
Key words:
- critical points /
- singular Hamiltonian systems /
- Homoclinic orbits
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