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By William T. Reid

A tremendous section of the learn of the qualitative nature of recommendations of differential equations might be traced to the well-known 1836 paper of Sturm [1), (here, as somewhere else all through this manuscript, numbers in sq. brackets seek advice from 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 one of those boundary challenge referred to as a "Sturm-Liouville problem," regarding, particularly, an creation to the examine of the asymptotic habit of solu tions of linear moment order differential equations by way of quintessential equations. within the sector century following the 1891 Gottingen dissertation [1) of Maxime Bacher (1867-1918), he was once 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, which have been in this case released as his recognized Leaons sur Zes methodes de Sturm [7).

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