Abstract

The main point of the present paper is to derive a limit-point criterion from which the criteria of Weyl [6], Friedrichs [3] and Sears [4] follow as special cases. This limit-point criterion is an immediate consequence of a Sturm comparison theorem. It is shown to be equivalent to the criterion of Weyl [6] when use is made of a Liouville-type transformation formula. Consider the Sturm-Liouville differential operator

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