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Sturm-Liouville Theory

Created
Created
2024 Sep 26 13:26
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Creator
Seonglae Cho
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Editor
Seonglae Cho
Edited
Edited
2024 Sep 26 13:26
Refs
Refs
Sturm-Liouville Theory Notion
Liouville Transformation
 
 
 
Sturm–Liouville theory
In mathematics and its applications, a Sturm–Liouville problem is a second-order linear ordinary differential equation of the form d d x [ p ( x ) d y d x ] + q ( x ) y = − λ w ( x ) y {\displaystyle {\frac {\mathrm {d} }{\mathrm {d} x}}\left[p(x){\frac {\mathrm {d} y}{\mathrm {d} x}}\right]+q(x)y=-\lambda w(x)y} for given functions p ( x ) {\displaystyle p(x)} , q ( x ) {\displaystyle q(x)} and w ( x ) {\displaystyle w(x)} , together with some boundary conditions at extreme values of x {\displaystyle x} . The goals of a given Sturm–Liouville problem are:
Sturm–Liouville theory
https://en.wikipedia.org/wiki/Sturm–Liouville_theory
 
 

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