In this article, we consider a discrete right-definite Sturm-Liouville problems with two squared eigenparameter-dependent boundary conditions. By constructing some new Lagrange-type identities and two fundamental functions, we obtain not only the existence, the simplicity, and the interlacing properties of the real eigenvalues, but also the oscillation properties, orthogonality of the eigenfunctions, and the expansion theorem. Finally, we also give a computation scheme for computing eigenvalues and eigenfunctions of specific eigenvalue problems.

中文翻译：

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具有两个平方特征参数相关边界条件的离散 Sturm-Liouville 问题的谱特性

在本文中，我们考虑具有两个平方特征参数相关边界条件的离散右定 Sturm-Liouville 问题。通过构造一些新的拉格朗日型恒等式和两个基本函数，我们不仅得到了实特征值的存在性、简单性和交织性质，而且还得到了本征函数的振荡性质、正交性和展开定理。最后，我们还给出了计算特定特征值问题的特征值和特征函数的计算方案。