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A minimax method for a class of Hamiltonian systems with singular potentials. (English) Zbl 0681.70018

Summary: This paper presents a minimax method which gives existence and multiplicity results for time periodic solutions of a class of Hamiltonian systems when a singular potential is present. The singularity satisfies the strong force condition of Gordon. When milder singularities are permitted a notion of generalized T-periodic solution is introduced and we get existence and multiplicity results for such solutions.

MSC:

70H05 Hamilton’s equations
37-XX Dynamical systems and ergodic theory
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[4] Degiovanni, M.; Giannoni, F.; Marino, A., Periodic solutions of dynamical systems with Newtonian type potentials, (Rabinowitz, P. H.; etal., Periodic Solutions of Hamiltonian Systems and Related Topics. Periodic Solutions of Hamiltonian Systems and Related Topics, NATO ASI Series, Vol. 209 (1987), Reidel: Reidel Dordrecht), 111-115
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