Equivalency for disconjugate operators

The solutions of the differential equation L(n)x + a(0)(t)x = 0, where L-n is a disconjugate operator and ao is of one sign, are studied according to their behavior as t --> infinity. We prove equivalence theorems between sol utions of this equation and its adjoint in terms of property A and property B. These theorems generalize the results known for n = 3 and for odd order binomial equations. Some applications are given too.