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A Sturm-Liouville Eigenvalue Problem

2.6

2.8

This Demonstration shows solutions to the Sturm–Liouville eigenvalue problem

ℒy=(xy')'+

y=−λσy

subject to the boundary conditions

y'(1)=0

and

y'(2)=0

This equation may be written as a Cauchy–Euler equation

y''+xy'+(λ+2)y=0

, where

λ+2>0

Solutions are of the form

y(x)=ccos

2πn

log2

log(x)

You can vary the parameters

and

The eigenvalues are

λ=

(log2)

-2

[1] M. Al-Gwaiz, Sturm–Liouville Theory and Its Applications, London: Springer, January 2008.

[2] A. Zettl, Sturm–Liouville Theory, Providence, RI: American Mathematical Society, 2005.

[3] M. L. Abell and J. P. Braselton, Differential Equations with Mathematica, 3rd ed., Boston: Elsevier, 2004.

[4] R. L. Herman, A Second Course in Ordinary Differential Equations: Dynamical Systems and Boundary Value Problems, Monograph, December 2008. (Oct 1, 2020) people.uncw.edu/hermanr/mat463/ODEBook/Book/ODE_Main.pdf.

Tania Mata, Rafael Fernandez, Tomas Garza, Rafael Fernandez

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