The problem of determining
sufficient conditions which that assure that all solutions of the second order equation
x′′+ q(t)x = 0 approach zero as t tends to infinity has been studied extensively since
1933. Several results have been given for generalizations of the basic linear
equation. In this paper a new technique is used to obtain further results for the
equation
(1)
The generality of the theorems developed is established by showing that a substantial
number of previously known results are immediate consequences of the work herein.
Of particular interest is the fact that three recent theorems by Burton and
Grimmer, which appeared in this journal, follow from the work contained in this
paper.
