A New Method of Solving the Index Problem for Sturm-Liouville Eigenvalues

Based on some recent results for interlacing eigenvalue intervals from 1-parameter families of sequences of eigenvalue inequalities, a new method is given to solving the index problem for Sturm-Liouville eigenvalues for coupled self-adjoint boundary conditions in the regular case. The key is a new characteristic principle for indices for Sturm-Liouville eigenvalues. The algorithm corresponding on the characteristic principle are discussed, and numerical examples are presented to illustrate the theoretical results and show that the algorithm is valid.