Oscillation and nonoscillation of solutions of second order linear differential equations with integrable coefficients

where a(t) is a locally integrable function of /. We call equation (1) oscillatory if all solutions of (1) have arbitrarily large zeros on [0, oo), otherwise, we say equation (1) is nonoscillatory. As a consequence of Sturm's Separation Theorem [21], if one of the solutions of (1) is oscillatory, then all of them are. The same is true for the nonoscillation of (1). The literature on second order linear oscillation is voluminous. The first such result is of course the classical theorem of Sturm which asserts that (2) a(t) ^ a0 > 0 => oscillation, and (3) a(t) S 0 => nonoscillation, where the inequalities in (2) and (3) are to be valid to all large /(2). Using the classical Euler's equation as the basic comparison equation :