Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems

Shinji Adachi

DOI: http://dx.doi.org/10.12775/TMNA.2005.014

Abstract


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 $\alpha\in (0,2)$.

Keywords


Singular Hamiltonian system; periodic solution; minimax theory

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