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Inverse problem for the differential pencil on an arbitrary graph with partial information given on the coefficients

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In this paper, a partial inverse problem for the quadratic Sturm–Liouville pencil on a geometrical graph of arbitrary structure is studied. We suppose that the coefficients of differential expressions are… Click to show full abstract

In this paper, a partial inverse problem for the quadratic Sturm–Liouville pencil on a geometrical graph of arbitrary structure is studied. We suppose that the coefficients of differential expressions are known a priori on all the graph edges except one, and recover the coefficients on the remaining edge, using a part of the spectrum. The results of the paper are uniqueness theorems and a constructive algorithm for solving the partial inverse problem.

Keywords: inverse problem; problem; differential pencil; graph; problem differential

Journal Title: Analysis and Mathematical Physics
Year Published: 2019

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