I'm concerned with a special problem of spectral analysis for a certain Sturm-Liouville-differential-operator, that is to say $L:=\frac{d^2}{dx^2}-q(x)$ and the spectrum $\sigma(L)$. While reading an article, I came across the following passage in the text where the author wrote about some properties of the eigenvalue $0$:
"... On the other hand, $0$ is always an eigenvalue of $L$, since $L\varphi'=0$, and it is simple and has a finite number of nodes."
Now, there is the main problem. I don't know in which sense the word "node" should be interpreted. I guess the number of linear independent solutions could be meant but I'm quite unsure with that.
I would be very thankful if anyone knows about that special usage or heard about that once before.
Edit:
$q(x):=F'(\varphi(x))$ for a $C^2$-Function $F$ and a bounded nonconstant function $\varphi \in C^2(-\infty,\infty)$ which satisfies the relation $F(\varphi)=\varphi''$. (The boundary conditions aren't mentioned, because they aren't needed-from the theory of Sturm-Liouville-Operators it is known that in case of limit circle at both end points no boundary conditions are necessary to obtain a self-adjoint operator on a suitable domain)