The intersection of the spectra of two Sturm-Liouville equations

This paper studies the intersection of the spectra for two Sturm-Liouville equations with general separated BCs and real coupled BCs. Under certain conditions, we proved that a two-dimensioned vectorial SLPs with separated BCs only has finitely many double eigenvalues and obtain a bound M-Q depending on Q(x) and its eigenvalues, which are larger than M-Q, are all simple. Finally, with the help of the obtained results, we conclude that the number of the same eigenvalue is finite for two one-dimensioned SLPs with general separated BCs or real coupled BCs. (C) 2012 Published by Elsevier Inc.