Abstract
We study the existence of non-collision periodic solutions with prescribed energy for the following singular Hamiltonian systems: $$ \begin{cases} \ddot q+\nabla V(q)=0, \\ \displaystyle \frac{1}{2}|\dot q|^2+V(q)=H. \end{cases} $$ In particular for the potential $V(q)\sim -1/{\rm dist} (q,D)^\alpha$, 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 $\alpha\in (0,2)$.
Citation
Shinji Adachi. "Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems." Topol. Methods Nonlinear Anal. 25 (2) 275 - 296, 2005.
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