In the present paper, a boundary value problem consisting of a Sturm–Liouville equation with boundary conditions dependent on the eigenparameter and discontinuous conditions inside the interval is investigated. We present new Prüfer substitutions and obtain the asymptotic form of eigenvalues, nodal points and nodal lengths. Then, we prove the uniqueness theorem for the solution of the inverse nodal problem, present a constructive procedure for the potential function by using nodal lengths. Finally, we study Lipschitz stability for the inverse problem.

中文翻译：

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新的Prüfer替代对不连续的Sturm–Liouville算子的逆节点问题

在本文中，研究了一个由Sturm-Liouville方程组成的边界值问题，其边界条件取决于特征参数和区间内的不连续条件。我们提出新的Prüfer替换，并获得特征值，节点和节点长度的渐近形式。然后，我们证明了逆节点问题解的唯一性定理，并通过使用节点长度为势函数提出了一个构造过程。最后，我们研究反问题的Lipschitz稳定性。