Verify that the periodic Sturm- Liouville system has a symmetric operator
The ones that I know is that the Sturm-Liouville periodic system is:
$L[y]=\lambda r(x)y=0$
$x_{1}< x< x_{2}$
$y(x_{1})=y(x_{2})$
${y}'(x_{1})={y}'(x_{2})$
where $L=D[p(x)D]+q(x)$ and where
$p(x_{1})=p(x_{2})$
As I show that an Sturm- Liouville equation of the form:
${y}''+\lambda y=0$
be the periodic Sturm- Liouville system.I've to confess that I'm a bit lost, can anyone give me a hint ?