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Periodic solutions to second order Hamiltonian systems in an unbounded potential well

Synopsis In this paper we give some results on the existence of periodic solutions to the second order Hamiltonian system: where and Ω is an open set of ℝn with non-empty bounded complement ℝn\Ω; we suppose V(t, x) is periodic in t, V(t, x)→ + ∞ as x → ∂Ω and V is super (or sub)-quadratic as |x| → + ∞.