= Sturm-Liouville equation
{c}
{title2=$-(py')'+qy=\lambda wy$}
A second-order differential equation in the displayed divergence form. Under the usual regular spectral assumptions, $p>0$, $w>0$, the coefficients have suitable regularity, and separated self-adjoint boundary conditions specify a <Sturm-Liouville problem>. Multiplying by $y$ and using zero endpoint values gives the <Rayleigh quotient> $\lambda=\int(py'^2+qy^2)dx/\int wy^2dx$ for a nonzero real <eigenfunction>. Sign conventions for the potential and eigenvalue vary; they must be read from the stated equation.
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