Abstract In this paper, partial inverse problems for the quadratic pencil of Sturm–Liouville operators on a graph with a loop are studied. These problems consist in recovering the pencil coefficients on one edge of the graph (a boundary edge or the loop) from spectral characteristics, while the coefficients on the other edges are known a priori. We obtain uniqueness theorems and constructive solutions for partial inverse problems.

中文翻译：

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带环图上二次微分铅笔的偏逆问题

摘要 本文研究了带环图上Sturm-Liouville算子二次铅笔的偏逆问题。这些问题包括从谱特征恢复图的一条边（边界边或环）上的铅笔系数，而其他边上的系数是先验已知的。我们获得了部分逆问题的唯一性定理和构造解。