I am looking to find a proof that eigenvalues are bounded below for the the general Sturm Liouville equation on an open region $ \Omega \subset \mathfrak R^d $ (perhaps with compact closure),
$Ly -\lambda \rho(\mathbf x) y = -\nabla \cdot \big( p(\mathbf x) \nabla y \big) + q(\mathbf x) y - \lambda \rho(\mathbf x) y = 0, \quad \mathbf x \in \Omega $
where $y $ is twice differentiable, $ p, \rho > 0 $ and boundary conditions on $ \partial\Omega $,
$\alpha(\mathbf s) y + \beta(\mathbf s) \frac{\partial y}{\partial n} = 0 $
($\alpha, \beta$ not both zero).
Can anyone help me find a clear treatment handling of this question?