# Inverse problems for higher order differential systems with regular singularities on star-type graphs

## DOI:

https://doi.org/10.5556/j.tkjm.46.2015.1754## Keywords:

Geometrical Graphs, Differential Operators, Inverse Spectral Problems## Abstract

We study an inverse spectral problem for arbitrary order ordinary differential equations on compact star-type graphs when differential equations have regular singularities at boundary vertices. As the main spectral characteristics we introduce and study the so-called Weyl-type matrices which are generalizations of the Weyl function (m-function) for the classical Sturm-Liouville operator. We provide a procedure for constructing the solution of the inverse problem and prove its uniqueness.## References

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*Tamkang Journal of Mathematics*,

*46*(3), 257–268. https://doi.org/10.5556/j.tkjm.46.2015.1754