A major portion of the study of the qualitative nature of solutions of differential equations may be traced to the famous 1836 paper of Sturm 1), (here, as elsewhere throughout this manuscript, numbers in square brackets refer to the bibliography at the end of this volume), dealing with oscilla tion and comparison theorems for linear homogeneous second order ordinary differential equations. The associated work of Liouville introduced a type of boundary problem known as a "Sturm-Liouville problem," involving, in particular, an introduction to the study of the asymptotic behavior of solu tions...