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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

  1. $p(x),q(x),r(x)$ are continuous on $[a,b]$
  2. $q(x)>0$ on $[a,b]$

then the problem as a unique solution.

Thanks!

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    There are already nice answers here. An alternative would be to apply more general results from elliptic PDE theory, or from Sturm-Liouville theory.2012-08-15

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