In this paper, we consider the inverse spectral problem for the impulsive Sturm–Liouville differential pencils on [0, π] with the Robin boundary conditions and the jump conditions at the point . We prove that two potentials functions on the whole interval and the parameters in the boundary and jump conditions can be determined from a set of eigenvalues for two cases: (i) the potentials given on and (ii) the potentials given on , where 0 < α < 1, respectively. Inverse spectral problems, Sturm–Liouville operator, spectrum, uniqueness.

中文翻译：

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带脉冲的Sturm-Liouville方程的二次铅笔的半反问题

在本文中，我们考虑在[0，  π ]上具有Robin边界条件和该点的跳跃条件的脉冲Sturm-Liouville微分铅笔的逆谱问题。我们证明了在整个区间上有两个势函数，并且可以从两种情况下的一组特征值确定边界条件和跳跃条件中的参数：（i）给出的势和（ii）给出的势，其中0 <  α  <1。反谱问题，Sturm–Liouville算子，谱，唯一性。