I ran across the following. In the text I was reading, it was left unproved. Can anyone help me see why it's true?
If the linear two-point boundary value problem \begin{cases} y''=p(x)y'+q(x)y+r(x)\\ y(a)=A\\ y(b)=B \end{cases} satisfies
- $p(x),q(x),r(x)$ are continuous on $[a,b]$
- $q(x)>0$ on $[a,b]$
then the problem as a unique solution.
Thanks!