On the zeros of solutions of Nth order linear differential equations

On the equivalence of oscillation and the existence of infinitely many conjugate points

“…Recently Ridenhour [10] has given conditions on equation (1.1) in terms of boundary-value functions under which he is able to obtain a characterization of the extremal solution for rj p (a) analogous to the characterization given by Leighton and Nehari in [6]. The purpose of this paper is to give conditions on equation (1.1) under which oscillation is equivalent to the existence of r) p (a) for each integer p ^ 1.…”

“…The conditions given here, although more restrictive than those in [10], are equivalent to those in [6] for n = 4. We shall make extensive use of several theorems given in [ 10].…”

Linear differential equations where nonoscillation is equivalent to eventual disconjugacy

“…License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use LINEAR DIFFERENTIAL EQUATIONS 369 2 is trivial when n = 3. If n > 3, p = 1, and k = 2, then Theorem 2.3 of [8] implies N y = oo, conclusion Suppose for now that p satisfies 1 < p < n -1. The cases where p = 1 or p = n -1 will be discussed later.…”

“…Definitions and agreements. By a solution of (1), we will always mean a nontrivial solution of (1 [8] in case k = 2 and 2 < p < n -2; however, no result in [8] immediately implies Lemma 2 when k = 2 and p = l or p = n -1. Lemma…”

On the sign of Green’s functions for multipoint boundary value problems

“…[10], [11], and [12] and the references therein) have been written establishing relations between different kinds of disconjugacy assumptions. Sections 2 and 3 deal with two-point and multipoint problems, respectively.…”