Conjugate points and simple zeros for ordinary linear differential equations

Abstract

with pi E C(a, b), has a nontrivial solution with n zeros, each being counted in accordance with its multiplicity, if and only if there is a solution with n distinct zeros on (a, b). Left as an open question in that paper was the question of whether the result remains true when the restriction that the interval be open is removed. The answer to this question is given in ?4 of this paper. In addition there is the problem of giving a more exact description to the solution with n distinct zeros, that is, does there exist a solution with exactly n distinct zeros all of which are simple? Also, can the first zero be specified? These latter two questions are answered in ?2, and more specifically by