The intersection of the spectra of two Sturm–Liouville equations

摘要

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 MQ depending on Q(x) and its eigenvalues, which are larger than MQ, 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.