Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems
Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems
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DOI：
10.12775/tmna.2005.014
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发表时间：
2005-06
影响因子：
0.7
通讯作者：
Shinji Adachi
中科院分区：
文献类型：
--
作者：
Shinji Adachi
我们研究了以下奇异Hamilton系统具有指定能量的非碰撞周期解的存在性：$$ \cases \ddot q+\nabla V（q）=0，\displaystyle \frac{1}{2}|\dot q| ^2 +V（q）=H。\endcases $$特别是对势$V（q）\sim-1/\text{\rm dist}（q，D）^\alpha$，其中奇异集$D$是$\mathbb R^N$的非空紧子集，我们证明了对所有$H> 0$和$\alpha\in（0，2）$存在非碰撞周期解.
We study the existence of non-collision periodic solutions with prescribed energy for the following singular Hamiltonian systems: $$ \cases \ddot q+\nabla V(q)=0, \\ \displaystyle \frac{1}{2}|\dot q|^2+V(q)=H. \endcases $$ In particular for the potential $V(q)\sim -1/\text{\rm dist} (q,D)^\alpha$, where the singular set $D$ is a non-empty compact subset of $\mathbb R^N$, we prove the existence of a non-collision periodic solution for all $H> 0$ and $\alpha\in (0,2)$.