具有固定能量的奇异Hamilton系统的新周期解
New Periodic Solutions of Singular Hamiltonian Systems with Fixed Energies
摘要：
利用带特殊约束的变分极小化方法和无约束的直接变分极小化方法，研究了具有奇异位势的二阶Hamilton系统$V\in C^2(R^n\backslash O,R)$和可能具有无界势阱的二阶Hamilton系统$V\in C^1(R^2\backslash O,R)$，证明了具有指定能量的非平凡周期解的存在性.我们的结果可以看作是Benci-Gluck-Ziller-Hayashi和Ambrosetti-Coti Zelati等著名定理的补充。
英文摘要：
By using the variational minimizing method with a special constraint and the direct variational minimizing method without constraint, we study second order Hamiltonian systems with a singular potential $V\in C^2(R^n\backslash O,R)$ and $V\in C^1(R^2\backslash O,R)$ which may have an unbounded potential well, and prove the existence of non-trivial periodic solutions with a prescribed energy. Our results can be regarded as some complements of the well-known Theorems of Benci-Gluck-Ziller-Hayashi and Ambrosetti-Coti Zelati and so on.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
