Algorithms for Solving Inverse Eigenvalue Problems for Sturm-Liouville Equations

Abstract

In the present paper we will consider the inverse eigenvalue problem for a Sturm-Liouville equation in so called impedance form,

$$\left( {{p^2}\left( x \right)u\prime \left( x \right)} \right)\prime + {w^2}{p^2}\left( x \right)u\left( x \right) = 0, 0 \leqslant x \leqslant L, p\left( x \right)> 0 $$

((1))

and with the following boundary conditions and nations for the eigenfrequencies.