We show that certain properties of positive solutions of disconjugate second order differential expressions imply the separation of the minimal and maximal operators determined by in where , -infty$">, i.e., the property that . This result will allow the development of several new sufficient conditions for separation and various inequalities associated with separation. Some of these allow for rapidly oscillating . It is shown in particular that expressions with solutions are separated, a property leading to a new proof and generalization of a 1971 separation criterion due to Everitt and Giertz. A final result shows that the disconjugacy of for some 0$ --> 0$"> implies the separation of .
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