  We discuss the occurrence of oscillatory solutions which decay to 0 as
$s\to+\infty$ for a class of perturbed second order ordinary differential
equations. As opposed to other results in the recent literature, the
perturbation is as small as desired in terms of its improper integrals and it
is independent of the coefficients of the non-oscillatory unperturbed equation.
This class of equations reveals thus a new pathology in the theory of perturbed
oscillations.
