Connecting orbits for a class of singular time periodic second order Hamiltonian systems

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We show existence of connecting orbits for a class of singular second-order Hamiltonian systems u¨ + Vu(t, u) = 0 , −∞ < t < ∞. where, as opposed to most of the existing literature, we assume that the potential V has, not one but any finite number of maxima of equal value. We use variational methods under the assumption that V (t, u) satisfies the so-called ”Strong-Force” condition at the singularity.