Necessary and Sufficient Condition for Quadratic Functional to be Positive Definite/Lemma 1

Theorem
If the function $\map h x$ satisfies the equation


 * $\displaystyle -\frac \d {\d x}\paren{Ph'}+Qh=0$

and the boundary conditions


 * $\map h a=\map h b=0$

then


 * $\displaystyle\int_a^b\paren{Ph'^2+Qh^2}\rd x=0$