Consider the Sturm-Liouville problem

$\displaystyle f'' + \lambda f' =0$

$\displaystyle f'(0) = 0, f'(1) = \beta f(1)$

For which values of $\displaystyle \beta$ does there exist an eigenvalue $\displaystyle \lambda$ in the interval $\displaystyle 0 <= \lambda <= \pi^2 /4$

All help is very appreciated or if someone can lead me in the right direction with this kind of problems!