Abstract We consider a new class of inverse problems on the recovery of the coefficients of differential equations from a finite set of eigenvalues of a boundary value problem with unseparated boundary conditions. A finite number of eigenvalues is possible only for problems in which the roots of the characteristic equation are multiple. The article describes solutions to such a problem for equations of the second, third, and fourth orders on a graph with three, four, and five edges. The inverse problem with an arbitrary number of edges is solved similarly.

中文翻译：

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在图上恢复微分方程系数的逆问题

摘要 我们考虑了一类新的逆问题，即从具有未分离边界条件的边界值问题的有限特征值集恢复微分方程的系数。有限数量的特征值仅适用于特征方程的根为多个的问题。本文描述了对具有三边、四边和五边的图上的二阶、三阶和四阶方程的此类问题的解决方案。类似地解决具有任意数量边的逆问题。