In this paper we prove the existence and decay of global solutions with
small initial data for a nonlinear second order ordinary differential equation of the form
xN(t) + (x? (t)) + g(x(t)) = f(x, x? , t), where (y) behaves as |y|ry, r ? 0, and g(x) as
|x|px, p ? 0, in a neighborhood of the origin (x, y) = (0, 0), and f(x, x? , t) is a nonlinear
pertubation.