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

Theorem
Let the function $\map h x$ satisfy the equation:


 * $-\map {\dfrac \d {\d x} } {P h'} + Q h = 0$

Let $\map h x$ have the boundary conditions:


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

Then:


 * $\displaystyle \int_a^b \paren {P h'^2 + Q h^2} \rd x = 0$