ABSTRACT
High-order linear differential inequalities are studied. Some new properties are established for them that are important for obtaining main results, In the case where the right-hand side has a quite general linear minorant, sufficient conditions are obtained for the given equation to have Property A or B. Effects of delay are investigated on existence of oscillatory solutions. Lemma 19.16 establishes two new properties of continuous functions that were not known earlier, and using the lemma efficient conditions of new type are obtained for existence of oscillatory solutions. In addition, sufficient conditions for existence of a positive solution are given.
