On the Number of the Zeros of Solutions of a Linear Differential Equation

Some classical estimates for the zeros of the solutions of third and fourth order linear differential equations, due to M. Hanan and to W. Leighton and Z. Nehari, respectively, are extended to the nth order case. Answering in a complete way to a conjecture of the last authors, it is proved that these estimates are, in any possible case, the sharpest ones.