By William T. Reid
A big part of the research of the qualitative nature of suggestions of differential equations should be traced to the recognized 1836 paper of Sturm [1), (here, as somewhere else all through this manuscript, numbers in sq. brackets confer with the bibliography on the finish of this volume), facing oscilla tion and comparability theorems for linear homogeneous moment order traditional differential equations. The linked paintings of Liouville brought a kind of boundary challenge referred to as a "Sturm-Liouville problem," regarding, specifically, an advent to the research of the asymptotic habit of solu tions of linear moment order differential equations via vital equations. within the area century following the 1891 Gottingen dissertation [1) of Maxime Bacher (1867-1918), he used to be instru psychological within the elaboration and extension of the oscillation, separation, and comparability theorems of Sturm, either in his many papers at the topic and his lectures on the Sorbonne in 1913-1914, that have been hence released as his well-known Leaons sur Zes methodes de Sturm [7).