Show that $\frac{d^2 y}{dx^2} - λ * y(x) = 0$ is a Sturm-Liouville problem, where λ is a constant and x is periodic with period 2π
I'm just struggling with how to put this into Sturm-Liouville form.
I know the
"x is periodic with period 2π"
is relating to $f(x) = f(x + 2π)$. But given that there is no value to $\frac{d y}{dx}$, there is no b(x), so B(x) is a constant, which kinda threw me off from an answer.
The notes I'm following have this on S-L:
Consider the general form $ \frac{d^2y}{dx^2} + b(x) \frac{d y}{dx} + c(x)y = λd(x)y $. Let B denote an antiderivative of b. This can be turned into Sturm-Liouville form, with conventional notation (with our choice of the sign of λ) (p(x)y ′)′ + q(x)y − λw (x)y = 0, where p(x) = e^B(x), q(x) = p(x)c(x) and w (x) = p(x)d(x).