  A novel method for finding the eigenvalues of a Sturm-Liouville problem is
developed. Following the minimalist approach the problem is transformed to a
single first-order differential equation with appropriate boundary conditions.
Although the resulting equation is nonlinear, its form allows to find the
general solution by adding a second part to a particular solution. This
splitting of the general solution in two parts involves the Schwarzian
derivative, hence the name of the approach. The eigenvalues that correspond to
acceptable solutions asymptotically can be found by requiring the second part
to correct the diverging behavior of the particular solution. The method can be
applied to many different areas of physics, such as the Schr\"odinger equation
in quantum mechanics and stability problems in fluid dynamics. Examples are
presented.
