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An inverse problem for differential pencils on graphs with a cycle. (English) Zbl 1318.34030

Second order differential equations with quadratic dependence on the eigenparameter are considered on compact graphs with a cycle. Using the ideas of the method of spectral mappings the following inverse problem is solved: To given spectral data, the potentials (or coefficients of the differential equations) can be recovered. Uniqueness is proved for this inverse problem and an algorithm is provided for constructing its solution.

MSC:

34A55 Inverse problems involving ordinary differential equations
34B45 Boundary value problems on graphs and networks for ordinary differential equations
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