Sturm-Liouville Theory

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


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
$$(k(x)V'(x))' + (g(x)r - l(x))V(x) = 0\quad for\;x \in (\alpha ,\beta ),$$
with the imposed boundary conditions
$$k(x)V'(x) - hV(x) = 0\quad for\;x = \alpha ,$$
$$k(x)V'(x) + HV(x) = 0\quad for\;x = \beta .$$


Fourier Series Successive Approximation Liouville Theory High Order Equation Expansion Theorem 
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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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