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Sturm-Liouville Theory

  • Jesper Lützen
Part of the Studies in the History of Mathematics and Physical Sciences book series (HISTORY, volume 15)

Abstract

1. In a series of articles dating from 1836–1837, Sturm and Liouville created a whole new subject in mathematical analysis. The theory, later known as Sturm-Liouville theory, deals with the general linear second-order differential equation
$$(k(x)V'(x))' + (g(x)r - l(x))V(x) = 0\quad for\;x \in (\alpha ,\beta ),$$
(1)
with the imposed boundary conditions
$$k(x)V'(x) - hV(x) = 0\quad for\;x = \alpha ,$$
(2)
$$k(x)V'(x) + HV(x) = 0\quad for\;x = \beta .$$
(3)

Keywords

Fourier Series Successive Approximation Liouville Theory High Order Equation Expansion Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Jesper Lützen
    • 1
  1. 1.Department of MathematicsUniversity of CopenhagenCopenhagenDenmark

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