Question

(Partial Differential Equations) - I'm trying to understand how a given example problem fits the general form of a Sturm-Loiuville Problem (SLP). Help is appreciated. More info below shortly.

Answer 1

\[\text {For} \ \lambda \ \in \ R \ \text{solve} \]\[y'' + \lambda y=0, \ y(0)=y'(\pi)=0\]

Answer 2

General form of SLP is:
\[[p(x)y']'+[q(x)+ \lambda r(x)]y=0\]How does this fit the general form?

Answer 3

@ganeshie8

Answer 4

p(x) = 1
q(x) = 0
r(x) = 1

since there are no x's in the DE, they represent constants

Answer 5

Left r(x)) = 1, let q(x) = 0, but I don't understand the p(x) bit and why there isn't an additional term?

Answer 6

Oh, nevermind, got it, thanks, guys.