Sturm-Liouville problem

A boundary value problem of the form d/dx[p(x)y'] + q(x)y + lambda*sigma(x)y = 0 together with boundary conditions, whose nontrivial solutions exist only for special values of lambda.

A (regular) Sturm-Liouville problem on $[a,b]$ consists of the equation $\dfrac{d}{dx}\big[p(x)y'\big]+q(x)y+\lambda\sigma(x)y=0$ , with $p,p',q,\sigma$ continuous, $p(x)>0$ and $\sigma(x)>0$ on $[a,b]$ , together with a pair of separated boundary conditions -- one at $a$ , one at $b$ , each a linear combination of $y$ and $y'$ there. A nontrivial solution $y$ exists only for specific values of $\lambda$ , called eigenvalues, each with a corresponding eigenfunction.