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Remarks on periodic solutions, with prescribed energy, for singular Hamiltonian systems. (English) Zbl 0678.34052
Summary: We search for periodic solutions, with prescribed energy, of Hamiltonian systems \(\dot x=H_ y\), \(\dot y=-H_ x(x,y\in {\mathbb{R}}^ n)\), where H(x,y) has the classical form: \(H(x,y)=| y|^ 2+V(x).\) We suppose that V(x)\(\to -\infty\) as \(x\to S(S\subset {\mathbb{R}}^ n)\), namely that the potential V is singular at \(x\in S\).

MSC:
34C25 Periodic solutions to ordinary differential equations
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