The finite spectrum of Sturm-Liouville problems with transmission conditions

We study the finite spectrum of Sturm-Liouville problems with transmission conditions. For any positive integer n, we construct a class of regular Sturm-Liouville problems with transmission conditions, which have exactly n eigenvalues, and these n eigenvalues can be located anywhere in the complex plane in non-self-adjoint case and anywhere along the real line in the self-adjoint case.