Abstract
We consider a class of second-order systems , with q(t) ∊ℝn, for which the potential energy V: ℝnS→ℝ admits a (possibly unbounded) singular set S ⊂ℝn and has a unique absolute maximum at 0 ∈ℝn. Under some conditions on S and V, we prove the existence of several solutions homoclinic to 0.