Connection between spectral and oscillation properties of differential-operator equations of arbitrary order. II. Applications of factorization and squaring

Factorization theorems of Frobenius and M. G. Krein-Heinz-Rellich type are established for infinite systems of differential equations of arbitrary even order on finite or infinite intervals. From here, Etgen and Pawlowski oscillation theorems, referring to second order equations, are generalized to the considered equations of order 2n and also a variant of a Sturm type comparison theorem is derived. An analogue of the oscillation theorem for discrete levels in the gap of the continuous spectrum is obtained for problems of both even and odd order.Translated from Teoriya Funktsii, Funktsional'nyi Analiz i Ikh Prilozheniya, No. 49, pp. 101–111, 1988.