A geometric approach to a result of Benci and Giannoni for Hamiltonian systems with singular potentials.

Zhu Daxin

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We consider a conservative second order Hamiltonian system $\ddot{q} + \nabla V (q) = 0$ in ℝ3 with a potential V having a global maximum at the origin and a line l ∩ 0 = ϑ as a set of singular points. Under a certain compactness condition on V at infinity and a strong force condition at singular points we study, by the use of variational methods and geometrical arguments, the existence of homoclinic solutions of the system.