Necessary and sufficient conditions for the oscillation of a second order linear differential equation

In this paper we give a necessary and sufficient condition for the oscillat ion of the second order linear differential equation y "(t) + p(t) y(t) = 0, t greater than or equal to t0, where p is a locally integrable function and either integral t0 infinity p(t)dt is an element of (-infinity, infinity) or integral t infinity[pn-1(s)]2 Qn-1(s, t)ds is an element of (-infinity, inf inity), for some n = 1, 2, ...., where P0(t) = integral t infinity p(s) ds, Pn(t) = integral t infinity Pn-1(s)2Qn-1(s, t) ds, Qn-1(s, t) = exp (Sigma j=0n-1 integral ts Pj(u) du), n = 1, 2, ... We give some applications which show how these results unify and imply some classical results in oscillation theory.