Relations among eigenvalues of left-definite Sturm–Liouville problems with coupled BCS and separated BCS

This paper deals with Left-Definite regular self-adjoint SLPs with coupled boundary conditions. It is obtained that, for a given eigenvalue λ∗λ∗ of Left-Definite regular SLPs with coupled BCs, there are some separated BCs also having λ∗λ∗ as an eigenvalue with the same index or indices. And then we can construct an algorithm for computing the index of a given eigenvalue for the Left-Definite SLPs with coupled boundary conditions.