Sturm-Liouville Equation

A second-order Ordinary Differential Equation

$${d\over dx}\left[{p(x){dy\over dx}}\right]+[\lambda w(x)-q(x)]y=0,$$

where $\lambda$ is a constant and $w(x)$ is a known function called either the density or Weighting Function. The solutions (with appropriate boundary conditions) of $\lambda$ are called Eigenvalues and the corresponding $u_\lambda(x)$ Eigenfunctions. The solutions of this equation satisfy important mathematical properties under appropriate boundary conditions (Arfken 1985).

See also Adjoint Operator, Self-Adjoint Operator

References

Arfken, G. ``Sturm-Liouville Theory--Orthogonal Functions.'' Ch. 9 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 497-538, 1985.