We introduce a function whose zeros, and only these zeros, are eigenvalues of the corresponding Sturm-Liouville problem. The boundary conditions of the problem depend continuously on the spectral parameter. Therefore, it makes sense to call the function thus constructed a characteristic function of the Sturm-Liouville problem (however, it is not a characteristic function in the ordinary sense). An investigation of the function thus obtained enables us to prove the solvability of the problem in question, to find the asymptotic behaviour of the eigenvalues, to obtain comparison theorems, and to introduce an indexing of the eigenvalues and the zeros of eigenfunctions in a natural way.

Bibliography: 31 titles.

我们引入了一个函数，它的零点，只有这些零点，才是对应的 Sturm-Liouville 问题的特征值。问题的边界条件持续依赖于谱参数。因此，将如此构造的函数称为Sturm-Liouville问题的特征函数是有道理的（但它不是通常意义上的特征函数）。对如此获得的函数的研究使我们能够证明所讨论问题的可解性，找到特征值的渐近行为，获得比较定理，并以自然的方式引入特征值的索引和特征函数的零点.

参考书目：31个标题。