Strong and Quasistrong Disconjugacy

Abstract

AbstractA complex linear homogeneous differential equation of the nth order is called strong disconjugate in a domain G if, for every n points z1,…, zn in G and for every set of positive integers, k1…, kl, k1 + … + kl = n, the only solution y(z) of the equation which satisfiesis the trivial one y(z) = 0. The equation y(n)(z) = 0 is strong disconjugate in the whole plane and for every other set of conditions of the form y(mk(zk) = 0, k = 1 , . . . , n, m1 ≤ m2... mn, there exist, in any given domain, points z1 , . . . , zn and nontrivial polynomials of degree smaller than n, which satisfy these conditions. An analogous results holds also for real disconjugate differential equations.