An -dimensional vectorial inverse nodal Sturm-Liouville problem with eigenparameter-dependent boundary conditions is studied. We show that if there exists an infinite sequence of eigenfunctions which are all vectorial functions of type (CZ), then the potential matrix and are simultaneously diagonalizable by the same unitary matrix . Subsequently, some multiplicity results of eigenvalues are obtained.

中文翻译：

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向量Sturm-Liouville问题的逆节点问题和特征值的多重性

一个-维矢量逆节点斯特姆-Liouville问题的与特征参数相关的边界条件进行了研究。我们表明，如果存在一个无限序列的本征函数它们是类型（CZ）的所有矢量的功能的，则潜在矩阵和是同时由同一个酉矩阵对角化。随后，获得一些特征值的多重结果。