The Sturm–Liouville equation is a particular second-order linear differential equation with boundary conditions that often occurs in the study of linear, separable partial differential equations.

# Questions tagged [sturm-liouville]

395 questions

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### Homogenuous Sturm Liouville problem (condtion for negative eigenvalues)

Consider the Sturm - Liouville problem:
$$y''+\lambda y=0,$$
$$ y(0)=c\pi y'(\pi)-y(\pi)=0$$
(a) Find the condition $c$ must satisfy, so that the problem has negative eigenvalues.
(b) How many are the negative eigenlaues (in case they…

Nikolaos Skout

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### Solve the following periodic problem Sturm-Liouville

Solve the following periodic problem
$$u_{t}-u_{xx}=0, \quad -\pi0$$
$$u(-\pi,t)=u(\pi,t), \quad u_{x}(-\pi,t)=u_{x}(\pi,t), \quad t\geq 0 $$
$$u(x,0)= \left\{ \begin{array}{lcc}
1 & -\pi\leq x\leq 0 \\
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CAMILO JOSE CANCIO MEZA

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### How to solve $y''(t)+λy(t)=0 $

How to solve this Sturm-Liouville problem:
$$y''(t)+λy(t)=0 $$
$$y(0)=y'(\pi) ,y'(0)=y(\pi)$$
Would really appreciate a solution or a significant hint because I couldn't find anything

PHOENIX3

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### Sturm-Liouville form question urgent

Hi guys so I have this differential of order 2 that I want to get to the Sturm-Liouville form by first finding the $p(x)$.
The form itself is : $(p(x).y'(x))'+q(x).y(x)=0$
And of course, it has equivalent other forms and definitions
And the exercise…

Zed zaki

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### Legendre's Equation, sturm liouville - eigenvalues/eigenfunction

Linear Differential Equation,Legendre's Equation, sturm liouville - eigenvalues/eigenfunction
Consider the linear differential operator:
$$ L = \frac{1}{4}(1+x^2)\frac{d^2}{dx^2}+\frac{1}{2}x(1+x^2)\frac{d}{dx}+a $$
acting on functions defined…

cisko

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