For large positive t, let co(t) be a positive continuous function correspondinig to which the differential equation (*) x"'+ W2 (t)x 0 has the following property: x'(t) -* 0, as t -* oo, holds for the derivative of every solutioni x(t) of (*). Then (*) will be called flat (all of its solutions "flatten out"; still, they can be "wobbly" and "large," as shown by the example w(t) = c/t, mentioned below for c> k). Since x(t) == o(t) is necessary for x'(t) ==o(1), the "frequency" 0(t) > 0 cannot be "too small" (for large t) if (*) is flat. In fact, (*) will have solutions satisfying x (t) t if the integral of t()2 (t) over const.? t 0. Crucial proves to be the limiting case e = 0, since the issue then involves the numerical value of the constant absorbed by the 0 of the assumption w (t) 0 (t-1). Put therefore [w] = lim sup tw (t), and assume that [w] < oo.t