show that $λ=0$ is an eigenvalue of the regular Sturm- Liouville system
$\frac{\mathrm{d} }{\mathrm{d} x}[p(x){y}']+\lambda r(x)y=0$
${y}'(0)=0$
${y}'(1)=0$
What I have done is this:
$\frac{\mathrm{d} }{\mathrm{d} x}[p(x){y}']+\lambda r(x)y=0$
$p(x){y}''+{p}'(x){y}'+\lambda r(x)y=0$
$\lambda =0$
$p(x){y}''+{p}'(x){y}'=0$
I've to confess that I'm a bit lost, can anyone give me a hint ?
