On certain comparison theorems for second order linear oscillation

It is shown that if (py')' + qy = 0 on ( 0, oo) is oscillatory then (pz')' + aqz = 0 is also oscillatory for functions satisfying a(t) - 1 and 2p(t)a'(t) - 3 f(s) a2(s)a (s) ds is nonincreasing.