Theory of a Higher-Order Sturm-Liouville Equation, Vladimir Kozlov; Vladimir Maz`ya

Автор: Levitan; I.S. Sargsjan
Название: Sturm—Liouville and Dirac Operators
ISBN: 0792309928 ISBN-13(EAN): 9780792309925
Издательство: Springer
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Описание: 'Et moi, ...- si j'avait su comment en revenir, One service mathematics has rendered the je n'y serais point allC: .' human. race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non- linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com- puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'ttre of this series.

Автор: William T. Reid; J. Burns; T. Herdman; C. Ahlbrand
Название: Sturmian Theory for Ordinary Differential Equations
ISBN: 0387905421 ISBN-13(EAN): 9780387905426
Издательство: Springer
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Описание: 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 of linear second order differential equations by the use of integral equations. In the quarter century following the 1891 Gottingen dissertation 1) of Maxime Bacher (1867-1918), he was instru- mental in the elaboration and extension of the oscillation, separation, and comparison theorems of Sturm, both in his many papers on the subject and his lectures at the Sorbonne in 1913-1914, which were subsequently published as his famous Leaons sur Zes methodes de Sturm 7).