On the oscillation of differential equations with an oscillatory coefficient

Abstract

We derive lower bounds for the distance between consecutive zeros of solutions of \[ ( ∗ ) y " + q ( t ) y = 0 ( * )\quad y" + q(t)y = 0 \] when q q takes both positive and negative values. We apply our results to the limit point/limit circle classifications of ( ∗ ) ( * ) .