Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems
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Singular Hamiltonian system, periodic solution, minimax theoryAbstrakt
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 $\alpha\in (0,2)$.Pobrania
Opublikowane
2005-06-01
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ADACHI, Shinji. Non-collision periodic solutions of prescribed energy problem for a class of singular Hamiltonian systems. Topological Methods in Nonlinear Analysis [online]. 1 czerwiec 2005, T. 25, nr 2, s. 275–296. [udostępniono 22.7.2024].
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